# Step-by-step Solution

## Derive the function $\ln\left(2x^2+4x\right)$ with respect to x

Go
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
Dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Videos

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

## Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(\ln\left(2x^2+4x\right)\right)$
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 $\displaystyle f'(x)=\frac{a'}{a}$

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

The derivative of a sum of two functions is the sum of the derivatives of each function

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

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

### Main topic:

Differential calculus

~ 0.82 seconds

### Struggling with math?

Access detailed step by step solutions to millions of problems, growing every day!