Calculus Examples

$z = \frac{a}{y^{9}} + b e^{y}$

Step 1

By the Sum Rule, the derivative of $\frac{a}{y^{9}} + b e^{y}$ with respect to $z$ is $\frac{d}{d z} [\frac{a}{y^{9}}] + \frac{d}{d z} [b e^{y}]$ .

$\frac{d}{d z} [\frac{a}{y^{9}}] + \frac{d}{d z} [b e^{y}]$

Step 2

Since $\frac{a}{y^{9}}$ is constant with respect to $z$ , the derivative of $\frac{a}{y^{9}}$ with respect to $z$ is $0$ .

$0 + \frac{d}{d z} [b e^{y}]$

Step 3

Since $b e^{y}$ is constant with respect to $z$ , the derivative of $b e^{y}$ with respect to $z$ is $0$ .

$0 + 0$

Step 4

Add $0$ and $0$ .

$0$