Calculus Examples

$x^{2} + y$

Step 1

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

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

Step 2

Since $x^{2}$ is constant with respect to $y$ , the derivative of $x^{2}$ with respect to $y$ is $0$ .

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

Step 3

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

$0 + 1$

Step 4

Add $0$ and $1$ .

$1$