Solusi - Derivatif

Menerapkan aturan perkalian turunan.

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

Turunan dari sebuah nilai konstan selalu nol.

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

Mengalikan sebuah angka dengan nol selalu menghasilkan nol.

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

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

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

Menghitung turunan dari sebuah pecahan.

$$4\times \frac{d}{dx}\left[\frac{{\left(xy\right)}^1}{2}\right]=4\times \frac{\frac{d}{dx}\left[{\left(xy\right)}^1\right]\times 2-{\left(xy\right)}^1\times \frac{d}{dx}\left[2\right]}{2^2}$$

Menghitung turunan dari sebuah fungsi pangkat.

$$4\times \frac{\frac{d}{dx}\left[{\left(xy\right)}^1\right]\times 2-{\left(xy\right)}^1\times \frac{d}{dx}\left[2\right]}{2^2}=4\times \frac{\left({\left(xy\right)}^1\times \left(\frac{d}{dx}\left[1\right]\times \ln \left(xy\right)+\frac{1}{xy}\times \frac{d}{dx}\left[xy\right]\right)\right)\times 2-{\left(xy\right)}^1\times \frac{d}{dx}\left[2\right]}{2^2}$$

Turunan dari sebuah nilai konstan selalu nol.

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

Menyederhanakan ekspresi aritmatika.

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

Turunan dari sebuah nilai konstan selalu nol.

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

Menerapkan aturan perkalian turunan.

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

Mengalikan sebuah angka dengan nol selalu menghasilkan nol.

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

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

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

Menyederhanakan ekspresi aritmatika.

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

Mengalikan sebuah angka dengan nol selalu menghasilkan nol.

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

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

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

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

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

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

$$4\times \frac{\left(xy\times \left(\frac{1}{xy}\times \left(1y+x\times \frac{d}{dx}\left[y\right]\right)\right)\right)\times 2}{4}=4\times \frac{\left(xy\times \left(\frac{1}{xy}\times \left(y+x\times \frac{d}{dx}\left[y\right]\right)\right)\right)\times 2}{4}$$