# Step-by-step Solution

## Find the derivative of $\ln\left(5x\right)$

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$\frac{1}{x}$

## Step-by-step Solution

Problem to solve:

$\frac{d}{dx}\left(\ln\left(5x\right)\right)$

Choose the solving method

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 $\displaystyle f'(x)=\frac{a'}{a}$

$\frac{\frac{d}{dx}\left(5x\right)}{5x}$

Learn how to solve differential calculus problems step by step online.

$\frac{\frac{d}{dx}\left(5x\right)}{5x}$

Learn how to solve differential calculus problems step by step online. Find the derivative of ln(5x). 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}. The derivative of the linear function times a constant, is equal to the constant. Simplifying.

$\frac{1}{x}$
SnapXam A2

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

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

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

$\frac{d}{dx}\left(\ln\left(5x\right)\right)$

### Main topic:

Differential Calculus

~ 0.18 s