Calculus Examples

$x + y^{2}$

Step 1

By the Sum Rule, the derivative of $x + y^{2}$ with respect to $y$ is $\frac{d}{d y} [x] + \frac{d}{d y} [y^{2}]$ .

$\frac{d}{d y} [x] + \frac{d}{d y} [y^{2}]$

Step 2

Since $x$ is constant with respect to $y$ , the derivative of $x$ with respect to $y$ is $0$ .

$0 + \frac{d}{d y} [y^{2}]$

Step 3

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

$0 + 2 y$

Step 4

Add $0$ and $2 y$ .

$2 y$