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Find the derivative of $\ln\left(\mathrm{sinh}\left(10x\right)\right)$

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 Final answer to the problem

$\frac{10\mathrm{cosh}\left(10x\right)}{\mathrm{sinh}\left(10x\right)}$
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 Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Find the derivative using the definition
• Find the derivative using the product rule
• Find the derivative using the quotient rule
• Find the derivative using logarithmic differentiation
• Find the derivative
• Integrate by partial fractions
• Product of Binomials with Common Term
• FOIL Method
• Integrate by substitution
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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 $\displaystyle f'(x)=\frac{a'}{a}$

$\frac{1}{\mathrm{sinh}\left(10x\right)}\frac{d}{dx}\left(\mathrm{sinh}\left(10x\right)\right)$

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

$\frac{1}{\mathrm{sinh}\left(10x\right)}\frac{d}{dx}\left(\mathrm{sinh}\left(10x\right)\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative of ln(sinh(10x)). 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}. Taking the derivative of hyperbolic sine. The derivative of the linear function times a constant, is equal to the constant. The derivative of the linear function is equal to 1.

 Final answer to the problem

$\frac{10\mathrm{cosh}\left(10x\right)}{\mathrm{sinh}\left(10x\right)}$

 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

SnapXam A2

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1
2
3
4
5
6
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.