Calculus Examples

$z = x^{y}$

Step 1

Differentiate both sides of the equation.

$\frac{d}{d x} (z) = \frac{d}{d x} (x^{y})$

Step 2

The derivative of $z$ with respect to $x$ is $z'$ .

$z'$

Step 3

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

$y x^{y - 1}$

Step 4

Reform the equation by setting the left side equal to the right side.

$z' = y x^{y - 1}$

Step 5

Replace $z'$ with $\frac{d z}{d x}$ .

$\frac{d z}{d x} = y x^{y - 1}$