Solusi - Derivatif

Turunan dari sebuah nilai konstan selalu nol.

$$\frac{d}{dx}\left[4\right]\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \frac{d}{dx}\left[{\left(2x^2+5\right)}^3\right]\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times \frac{d}{dx}\left[4x\right]=0{\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \frac{d}{dx}\left[{\left(2x^2+5\right)}^3\right]\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times \frac{d}{dx}\left[4x\right]$$

Menghitung turunan dari sebuah fungsi pangkat.

$$0{\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \frac{d}{dx}\left[{\left(2x^2+5\right)}^3\right]\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times \frac{d}{dx}\left[4x\right]=0{\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(\frac{d}{dx}\left[3\right]\times \ln \left(2x^2+5\right)+\frac{3}{2x^2+5}\times \frac{d}{dx}[2x^2+5]\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times \frac{d}{dx}\left[4x\right]$$

Menerapkan aturan perkalian turunan.

$$0{\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(\frac{d}{dx}\left[3\right]\times \ln \left(2x^2+5\right)+\frac{3}{2x^2+5}\times \frac{d}{dx}[2x^2+5]\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times \frac{d}{dx}\left[4x\right]=0{\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(\frac{d}{dx}\left[3\right]\times \ln \left(2x^2+5\right)+\frac{3}{2x^2+5}\times \frac{d}{dx}[2x^2+5]\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\left(\frac{d}{dx}\left[4\right]\times x+4\times \frac{d}{dx}\left[x\right]\right)$$

Turunan dari sebuah nilai konstan selalu nol.

$$0{\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(\frac{d}{dx}\left[3\right]\times \ln \left(2x^2+5\right)+\frac{3}{2x^2+5}\times \frac{d}{dx}[2x^2+5]\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\left(\frac{d}{dx}\left[4\right]\times x+4\times \frac{d}{dx}\left[x\right]\right)=0{\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(\frac{d}{dx}\left[3\right]\times \ln \left(2x^2+5\right)+\frac{3}{2x^2+5}\times \frac{d}{dx}[2x^2+5]\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\left(0x+4\times \frac{d}{dx}\left[x\right]\right)$$

Mengalikan sebuah angka dengan nol selalu menghasilkan nol.

$$0{\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(\frac{d}{dx}\left[3\right]\times \ln \left(2x^2+5\right)+\frac{3}{2x^2+5}\times \frac{d}{dx}[2x^2+5]\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\left(0x+4\times \frac{d}{dx}\left[x\right]\right)=0{\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(\frac{d}{dx}\left[3\right]\times \ln \left(2x^2+5\right)+\frac{3}{2x^2+5}\times \frac{d}{dx}[2x^2+5]\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\left(0+4\times \frac{d}{dx}\left[x\right]\right)$$

Menambahkan nol ke sebuah angka, yang tidak mengubah nilai angka tersebut.

$$0{\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(\frac{d}{dx}\left[3\right]\times \ln \left(2x^2+5\right)+\frac{3}{2x^2+5}\times \frac{d}{dx}[2x^2+5]\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\left(0+4\times \frac{d}{dx}\left[x\right]\right)=0{\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(\frac{d}{dx}\left[3\right]\times \ln \left(2x^2+5\right)+\frac{3}{2x^2+5}\times \frac{d}{dx}[2x^2+5]\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times \left(4\times \frac{d}{dx}\left[x\right]\right)$$

Turunan dari suatu variabel terhadap dirinya sendiri selalu sama dengan satu.

$$0{\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(\frac{d}{dx}\left[3\right]\times \ln \left(2x^2+5\right)+\frac{3}{2x^2+5}\times \frac{d}{dx}[2x^2+5]\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times \left(4\times \frac{d}{dx}\left[x\right]\right)=0{\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(\frac{d}{dx}\left[3\right]\times \ln \left(2x^2+5\right)+\frac{3}{2x^2+5}\times \frac{d}{dx}[2x^2+5]\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times \left(4\times 1\right)$$

Mengalikan sebuah angka dengan satu, yang tidak mengubah nilai angka tersebut.

$$0{\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(\frac{d}{dx}\left[3\right]\times \ln \left(2x^2+5\right)+\frac{3}{2x^2+5}\times \frac{d}{dx}[2x^2+5]\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times \left(4\times 1\right)=0{\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(\frac{d}{dx}\left[3\right]\times \ln \left(2x^2+5\right)+\frac{3}{2x^2+5}\times \frac{d}{dx}[2x^2+5]\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4$$

Turunan dari sebuah nilai konstan selalu nol.

$$0{\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(\frac{d}{dx}\left[3\right]\times \ln \left(2x^2+5\right)+\frac{3}{2x^2+5}\times \frac{d}{dx}[2x^2+5]\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4=0{\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0\times \ln \left(2x^2+5\right)+\frac{3}{2x^2+5}\times \frac{d}{dx}[2x^2+5]\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4$$

Menerapkan aturan penjumlahan turunan.

$$0{\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0\times \ln \left(2x^2+5\right)+\frac{3}{2x^2+5}\times \frac{d}{dx}[2x^2+5]\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4=0{\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0\times \ln \left(2x^2+5\right)+\frac{3}{2x^2+5}\times \left(\frac{d}{dx}\left[2x^2\right]+\frac{d}{dx}\left[5\right]\right)\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4$$

Mengalikan sebuah angka dengan nol selalu menghasilkan nol.

$$0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0\times \ln \left(2x^2+5\right)+\frac{3}{2x^2+5}\times \left(\frac{d}{dx}\left[2x^2\right]+\frac{d}{dx}\left[5\right]\right)\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4=0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0+\frac{3}{2x^2+5}\times \left(\frac{d}{dx}\left[2x^2\right]+\frac{d}{dx}\left[5\right]\right)\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4$$

Menerapkan aturan perkalian turunan.

$$0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0+\frac{3}{2x^2+5}\times \left(\frac{d}{dx}\left[2x^2\right]+\frac{d}{dx}\left[5\right]\right)\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4=0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0+\frac{3}{2x^2+5}\times \left(\left(\frac{d}{dx}\left[2\right]\times x^2+2\times \frac{d}{dx}\left[x^2\right]\right)+\frac{d}{dx}\left[5\right]\right)\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4$$

Turunan dari sebuah nilai konstan selalu nol.

$$0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0+\frac{3}{2x^2+5}\times \left(\left(\frac{d}{dx}\left[2\right]\times x^2+2\times \frac{d}{dx}\left[x^2\right]\right)+\frac{d}{dx}\left[5\right]\right)\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4=0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0+\frac{3}{2x^2+5}\times \left(\left(0x^2+2\times \frac{d}{dx}\left[x^2\right]\right)+\frac{d}{dx}\left[5\right]\right)\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4$$

Mengalikan sebuah angka dengan nol selalu menghasilkan nol.

$$0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0+\frac{3}{2x^2+5}\times \left(\left(0x^2+2\times \frac{d}{dx}\left[x^2\right]\right)+\frac{d}{dx}\left[5\right]\right)\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4=0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0+\frac{3}{2x^2+5}\times \left(\left(0+2\times \frac{d}{dx}\left[x^2\right]\right)+\frac{d}{dx}\left[5\right]\right)\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4$$

Menambahkan nol ke sebuah angka, yang tidak mengubah nilai angka tersebut.

$$0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0+\frac{3}{2x^2+5}\times \left(\left(0+2\times \frac{d}{dx}\left[x^2\right]\right)+\frac{d}{dx}\left[5\right]\right)\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4=0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0+\frac{3}{2x^2+5}\times \left(2\times \frac{d}{dx}\left[x^2\right]+\frac{d}{dx}\left[5\right]\right)\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4$$

Menghitung turunan dari x dipangkatkan dengan n.

$$0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0+\frac{3}{2x^2+5}\times \left(2\times \frac{d}{dx}\left[x^2\right]+\frac{d}{dx}\left[5\right]\right)\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4=0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0+\frac{3}{2x^2+5}\times \left(2\times \left(2x^{2-1}\right)+\frac{d}{dx}\left[5\right]\right)\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4$$

Mengurangkan satu dari sebuah angka.

$$0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0+\frac{3}{2x^2+5}\times \left(2\times \left(2x^{2-1}\right)+\frac{d}{dx}\left[5\right]\right)\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4=0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0+\frac{3}{2x^2+5}\times \left(2\times \left(2x^1\right)+\frac{d}{dx}\left[5\right]\right)\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4$$

Perkalian dapat dikelompokkan secara berbeda, tetapi hasilnya tetap sama.

$$0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0+\frac{3}{2x^2+5}\times \left(2\times \left(2x^1\right)+\frac{d}{dx}\left[5\right]\right)\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4=0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0+\frac{3}{2x^2+5}\times \left(\left(2\times 2\right)\times x^1+\frac{d}{dx}\left[5\right]\right)\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4$$

Mengalikan dua bilangan bulat bersama-sama.

$$0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0+\frac{3}{2x^2+5}\times \left(\left(2\times 2\right)\times x^1+\frac{d}{dx}\left[5\right]\right)\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4=0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0+\frac{3}{2x^2+5}\times \left(4x^1+\frac{d}{dx}\left[5\right]\right)\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4$$

Turunan dari sebuah nilai konstan selalu nol.

$$0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0+\frac{3}{2x^2+5}\times \left(4x^1+\frac{d}{dx}\left[5\right]\right)\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4=0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\left(0+\frac{3}{2x^2+5}\times \left(4x^1+0\right)\right)\right)\times \left(4x\right)+4{\left(2x^2+5\right)}^3\times 4$$

Menambahkan nol ke sebuah angka, yang tidak mengubah nilai angka tersebut.

$$0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\times \left(0+\frac{3}{2x^2+5}\times \left(4x^1+0\right)\right)\right)\times \left(4x\right)+4\times {\left(2x^2+5\right)}^3\times 4=0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\times \left(\frac{3}{2x^2+5}\times \left(4x^1+0\right)\right)\right)\times \left(4x\right)+4\times {\left(2x^2+5\right)}^3\times 4$$

Menyederhanakan ekspresi aritmatika.

$$0\times {\left(2x^2+5\right)}^3\times \left(4x\right)+4\times \left({\left(2x^2+5\right)}^3\times \left(\frac{3}{2x^2+5}\times \left(4x^1+0\right)\right)\right)\times \left(4x\right)+4\times {\left(2x^2+5\right)}^3\times 4=0+4\times \left({\left(2x^2+5\right)}^3\times \left(\frac{3}{2x^2+5}\times \left(4x^1+0\right)\right)\right)\times \left(4x\right)+4\times {\left(2x^2+5\right)}^3\times 4$$

Menambahkan nol ke sebuah angka, yang tidak mengubah nilai angka tersebut.

$$0+4\times \left({\left(2x^2+5\right)}^3\times \left(\frac{3}{2x^2+5}\times \left(4x^1+0\right)\right)\right)\times \left(4x\right)+4\times {\left(2x^2+5\right)}^3\times 4=0+4\times \left({\left(2x^2+5\right)}^3\times \left(\frac{3}{2x^2+5}\times \left(4x^1\right)\right)\right)\times \left(4x\right)+4\times {\left(2x^2+5\right)}^3\times 4$$

Menyederhanakan ekspresi aritmatika.

$$0+4\times \left({\left(2x^2+5\right)}^3\times \left(\frac{3}{2x^2+5}\times \left(4x^1\right)\right)\right)\times \left(4x\right)+4\times {\left(2x^2+5\right)}^3\times 4=0+4\times \left({\left(2x^2+5\right)}^3\times \left(\frac{3}{2x^2+5}\times \left(4x^1\right)\right)\right)\times \left(4x\right)+16{\left(2x^2+5\right)}^3$$

Menambahkan nol ke sebuah angka, yang tidak mengubah nilai angka tersebut.

$$0+4\times \left({\left(2x^2+5\right)}^3\times \left(\frac{3}{2x^2+5}\times \left(4x^1\right)\right)\right)\times \left(4x\right)+16{\left(2x^2+5\right)}^3=4\times \left({\left(2x^2+5\right)}^3\times \left(\frac{3}{2x^2+5}\times \left(4x^1\right)\right)\right)\times \left(4x\right)+16{\left(2x^2+5\right)}^3$$

Menyederhanakan ekspresi aritmatika.

$$4\times \left({\left(2x^2+5\right)}^3\times \left(\frac{3}{2x^2+5}\times \left(4x^1\right)\right)\right)\times \left(4x\right)+16{\left(2x^2+5\right)}^3=4\times \left({\left(2x^2+5\right)}^3\times \left(\frac{3}{2x^2+5}\times \left(4x\right)\right)\right)\times \left(4x\right)+16{\left(2x^2+5\right)}^3$$

Menyederhanakan ekspresi aritmatika.

$$4\times \left({\left(2x^2+5\right)}^3\times \left(\frac{3}{2x^2+5}\times \left(4x\right)\right)\right)\times \left(4x\right)+16{\left(2x^2+5\right)}^3=4\times \left({\left(2x^2+5\right)}^3\times \left(\frac{12x}{2x^2+5}\right)\right)\times \left(4x\right)+16{\left(2x^2+5\right)}^3$$

Menyederhanakan ekspresi aritmatika.

$$4\times \left({\left(2x^2+5\right)}^3\times \left(\frac{12x}{2x^2+5}\right)\right)\times \left(4x\right)+16{\left(2x^2+5\right)}^3=4\times \left(12x{\left(2x^2+5\right)}^2\right)\times \left(4x\right)+16{\left(2x^2+5\right)}^3$$

Menyederhanakan ekspresi aritmatika.

$$4\times \left(12x{\left(2x^2+5\right)}^2\right)\times \left(4x\right)+16{\left(2x^2+5\right)}^3=192x^2{\left(2x^2+5\right)}^2+16{\left(2x^2+5\right)}^3$$