Calculus Examples

$z^{\ln (4)} + \ln (3)$

Step 1

By the Sum Rule, the derivative of $z^{\ln (4)} + \ln (3)$ with respect to $z$ is $\frac{d}{d z} [z^{\ln (4)}] + \frac{d}{d z} [\ln (3)]$ .

$\frac{d}{d z} [z^{\ln (4)}] + \frac{d}{d z} [\ln (3)]$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d z} [z^{n}]$ is $n z^{n - 1}$ where $n = \ln (4)$ .

$\ln (4) z^{\ln (4) - 1} + \frac{d}{d z} [\ln (3)]$

Step 3

Since $\ln (3)$ is constant with respect to $z$ , the derivative of $\ln (3)$ with respect to $z$ is $0$ .

$\ln (4) z^{\ln (4) - 1} + 0$

Step 4

Simplify.

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Step 4.1

Add $\ln (4) z^{\ln (4) - 1}$ and $0$ .

$\ln (4) z^{\ln (4) - 1}$

Step 4.2

Reorder the factors of $\ln (4) z^{\ln (4) - 1}$ .

$z^{\ln (4) - 1} \ln (4)$