# Use exponential and logarithmic differentiation to find the derivatives of the f

Use exponential and logarithmic differentiation to find the derivatives of the following function:
$5{x}^{x-3}$
You can still ask an expert for help

## Want to know more about Derivatives?

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Anonym
Step 1
Given,
$5{x}^{x-3}$
Step 2
Taking logrithmic on both sides
$\mathrm{ln}y=\mathrm{ln}\left(5{x}^{x-3}\right)$
Using the product rule of the derivative.
$\frac{1}{y}\frac{dy}{dx}=\left(x-3\right)\frac{d}{dx}\left(\mathrm{ln}\left(5x\right)\right)+\left(\mathrm{ln}\left(5x\right)\right)\frac{d}{dx}\left(x-3\right)$
$\frac{1}{y}\frac{dy}{dx}=\left(x-3\right)\left(\frac{1}{5x}\left(5\right)\right)+\left(\mathrm{ln}\left(5x\right)\right)\left(1\right)$
$\frac{1}{y}\frac{dy}{dx}=\left(x-3\right)\left(\frac{1}{x}\right)+\mathrm{ln}\left(5x\right)$
$\frac{1}{y}\frac{dy}{dx}=\frac{\left(x-3\right)}{x}+\mathrm{ln}\left(5x\right)$
$\frac{dy}{dx}=y\left[\frac{\left(x-3\right)}{x}+\mathrm{ln}\left(5x\right)\right]$
$\frac{dy}{dx}=5{x}^{x-3}\left[\frac{\left(x-3\right)}{x}+\mathrm{ln}\left(5x\right)\right]$