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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 

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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)}. Multiply the fraction and term.

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

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Find the derivativeFind derivative of 2lnsin5x using the product ruleFind derivative of 2lnsin5x using the quotient ruleFind derivative of 2lnsin5x using logarithmic differentiation

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5
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7
8
9
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

### Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.