Solusi - Derivatif

n x^{n - 1} + \frac{- 1 \times \frac{d}{d x} [n]}{{(n + 1)}^{2}}

n x^{n - 1}+\frac{-1\times \frac{d}{dx}[n]}{\left(n + 1\right)^{2}}

Lihat langkah

Penjelasan langkah demi langkah

1. Selesaikan turunan

Menerapkan aturan penjumlahan turunan.

$\frac{d}{d x} [x^{n} + \frac{1}{n + 1}] = \frac{d}{d x} [x^{n}] + \frac{d}{d x} [\frac{1}{n + 1}]$

Menghitung turunan dari x dipangkatkan dengan n.

$\frac{d}{d x} [x^{n}] + \frac{d}{d x} [\frac{1}{n + 1}] = n x^{n - 1} + \frac{d}{d x} [\frac{1}{n + 1}]$

Menghitung turunan dari sebuah pecahan.

$n x^{n - 1} + \frac{d}{d x} [\frac{1}{n + 1}] = n x^{n - 1} + \frac{\frac{d}{d x} [1] \times (n + 1) - 1 \times \frac{d}{d x} [n + 1]}{{(n + 1)}^{2}}$

Turunan dari sebuah nilai konstan selalu nol.

$n x^{n - 1} + \frac{\frac{d}{d x} [1] \times (n + 1) - 1 \times \frac{d}{d x} [n + 1]}{{(n + 1)}^{2}} = n x^{n - 1} + \frac{0 (n + 1) - 1 \times \frac{d}{d x} [n + 1]}{{(n + 1)}^{2}}$

Menerapkan aturan penjumlahan turunan.

$n x^{n - 1} + \frac{0 \times (n + 1) - 1 \times \frac{d}{d x} [n + 1]}{{(n + 1)}^{2}} = n x^{n - 1} + \frac{0 \times (n + 1) - 1 (\frac{d}{d x} [n] + \frac{d}{d x} [1])}{{(n + 1)}^{2}}$

Mengalikan sebuah angka dengan nol selalu menghasilkan nol.

$n x^{n - 1} + \frac{0 \times (n + 1) - 1 (\frac{d}{d x} [n] + \frac{d}{d x} [1])}{{(n + 1)}^{2}} = n x^{n - 1} + \frac{0 - 1 (\frac{d}{d x} [n] + \frac{d}{d x} [1])}{{(n + 1)}^{2}}$

Turunan dari sebuah nilai konstan selalu nol.

$n x^{n - 1} + \frac{0 - 1 (\frac{d}{d x} [n] + \frac{d}{d x} [1])}{{(n + 1)}^{2}} = n x^{n - 1} + \frac{0 - 1 (\frac{d}{d x} [n] + 0)}{{(n + 1)}^{2}}$

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

$n x^{n - 1} + \frac{0 - 1 (\frac{d}{d x} [n] + 0)}{{(n + 1)}^{2}} = n x^{n - 1} + \frac{- 1 (\frac{d}{d x} [n] + 0)}{{(n + 1)}^{2}}$

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

$n x^{n - 1} + \frac{- 1 (\frac{d}{d x} [n] + 0)}{{(n + 1)}^{2}} = n x^{n - 1} + \frac{- 1 \times \frac{d}{d x} [n]}{{(n + 1)}^{2}}$

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Ever wondered how to predict the future? Derivatives are your crystal ball!

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In short, derivatives are like a secret code to understanding change and making predictions in real life. So let's crack this code together and become masters of our futures!

Istilah dan topik

Derivative

Solusi - Derivatif

Penjelasan langkah demi langkah

1. Selesaikan turunan

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