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# Find the derivative using the product rule [x]

### Videos

$\frac{2\left(x+5\right)-\left(2x+1\right)}{\left(x+5\right)^2}\left(3x-1\right)+\frac{3\left(2x+1\right)}{x+5}$

## Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(\frac{2x+1}{x+5}\cdot \left(3x-1\right)\right)$
1

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\frac{2x+1}{x+5}$ and $g=3x-1$

$\left(3x-1\right)\frac{d}{dx}\left(\frac{2x+1}{x+5}\right)+\frac{2x+1}{x+5}\cdot\frac{d}{dx}\left(3x-1\right)$

$\frac{2\left(x+5\right)-\left(2x+1\right)}{\left(x+5\right)^2}\left(3x-1\right)+\frac{3\left(2x+1\right)}{x+5}$
$\frac{d}{dx}\left(\frac{2x+1}{x+5}\cdot \left(3x-1\right)\right)$

### Main topic:

Differential calculus

~ 0.37 seconds