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# Find the derivative of $2\ln\left(\sin\left(5x\right)\right)$

## Step-by-step Solution

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### Videos

$10\cot\left(5x\right)$
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## Step-by-step Solution

Problem to solve:

$\frac{d}{dx}\left(2\ln\left(\sin\left(5x\right)\right)\right)$

Specify the solving method

1

The derivative of a function multiplied by a constant ($2$) is equal to the constant times the derivative of the function

$2\frac{d}{dx}\left(\ln\left(\sin\left(5x\right)\right)\right)$

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

$2\frac{d}{dx}\left(\ln\left(\sin\left(5x\right)\right)\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative of 2ln(sin(5x)). The derivative of a function multiplied by a constant (2) is equal to the constant times the derivative of the function. 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 sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}. The derivative of the linear function times a constant, is equal to the constant.

$10\cot\left(5x\right)$

### Explore different ways to solve this problem

Find the derivativeProduct ruleQuotient ruleLogarithmic differentiation
SnapXam A2

### beta Got another answer? Verify it!

Go!
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0
a
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u
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x
y
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.
(◻)
+
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×
◻/◻
/
÷
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

$\frac{d}{dx}\left(2\ln\left(\sin\left(5x\right)\right)\right)$

### Main topic:

Differential Calculus

~ 0.05 s