Calculus Examples

$y^{2} = x$

Step 1

Differentiate both sides of the equation.

$\frac{d}{d y} (y^{2}) = \frac{d}{d y} (x)$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d y} [y^{n}]$ is $n y^{n - 1}$ where $n = 2$ .

$2 y$

Step 3

Rewrite $\frac{d}{d y} [x]$ as $x'$ .

$x'$

Step 4

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

$2 y = x'$

Step 5

Rewrite the equation as $x' = 2 y$ .

$x' = 2 y$

Step 6

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

$\frac{d x}{d y} = 2 y$