Calculus Examples

$y x^{y - 1}$

Step 1

Since $y$ is constant with respect to $x$ , the derivative of $y x^{y - 1}$ with respect to $x$ is $y \frac{d}{d x} [x^{y - 1}]$ .

$y \frac{d}{d x} [x^{y - 1}]$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = y - 1$ .

$y ((y - 1) x^{y - 1 - 1})$

Step 3

Simplify the expression.

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Step 3.1

Subtract $1$ from $- 1$ .

$y ((y - 1) x^{y - 2})$

Step 3.2

Reorder the factors of $y ((y - 1) x^{y - 2})$ .

$x^{y - 2} y (y - 1)$