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\frac{d}{dx}\left(\ln\left(2x^2+4x\right)\right)

Find the derivative of ln(2x^2+4x)

Answer

$\frac{2\frac{d}{dx}\left(x^2\right)+4}{4x+2x^2}$

Step-by-step explanation

Problem

$\frac{d}{dx}\left(\ln\left(2x^2+4x\right)\right)$
1

The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$

$\frac{1}{4x+2x^2}\cdot\frac{d}{dx}\left(4x+2x^2\right)$

Unlock this step-by-step solution!

Answer

$\frac{2\frac{d}{dx}\left(x^2\right)+4}{4x+2x^2}$
$\frac{d}{dx}\left(\ln\left(2x^2+4x\right)\right)$

Main topic:

Differential calculus

Used formulas:

4. See formulas

Time to solve it:

~ 0.79 seconds