# What is the derivative of  e^(x^3)+log_5(pi)?

Mar 3, 2018

$\frac{d}{\mathrm{dx}} {e}^{{x}^{3}} + {\log}_{5} \left(\pi\right) = 3 {x}^{2} {e}^{{x}^{3}}$

#### Explanation:

The ${\log}_{5} \left(\pi\right)$ is a constant, so the derivative of the function can be turned down to a simpler $\frac{d}{\mathrm{dx}} {e}^{{x}^{3}}$.

Let $y$ be equal to ${e}^{{x}^{3}}$. Take the natural logarithm of both sides.

$\ln y = {x}^{3} \cdot \ln e$
$\ln y = {x}^{3}$

Differentiate both :

$\frac{\mathrm{dy}}{\mathrm{dx}} \frac{1}{y} = 3 {x}^{2}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = y \cdot 3 {x}^{2} = 3 {x}^{2} {e}^{{x}^{3}}$, so

$\textcolor{b l u e}{\frac{d}{\mathrm{dx}} {e}^{{x}^{3}} + {\log}_{5} \left(\pi\right) = 3 {x}^{2} {e}^{{x}^{3}}}$.