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

Derive the function (2x+1)/(x+5)(3x-1) with respect to x

Answer

$\frac{3+6x}{5+x}+\left(3x-1\right)\frac{2\left(5+x\right)-\left(1+2x\right)}{\left(5+x\right)^2}$

Step-by-step explanation

Problem

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

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

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

Unlock this step-by-step solution!

Answer

$\frac{3+6x}{5+x}+\left(3x-1\right)\frac{2\left(5+x\right)-\left(1+2x\right)}{\left(5+x\right)^2}$
$\frac{d}{dx}\left(\frac{2x+1}{x+5}\cdot \left(3x-1\right)\right)$

Main topic:

Differential calculus

Used formulas:

5. See formulas

Time to solve it:

0.34 seconds