Calculus Examples

$y = 4 x^{3} + 2 x^{2}$

Step 1

By the Sum Rule, the derivative of $4 x^{3} + 2 x^{2}$ with respect to $y$ is $\frac{d}{d y} [4 x^{3}] + \frac{d}{d y} [2 x^{2}]$ .

$\frac{d}{d y} [4 x^{3}] + \frac{d}{d y} [2 x^{2}]$

Step 2

Since $4 x^{3}$ is constant with respect to $y$ , the derivative of $4 x^{3}$ with respect to $y$ is $0$ .

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

Step 3

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

$0 + 0$

Step 4

Add $0$ and $0$ .

$0$