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Find the derivative of $\mathrm{coth}\left(\ln\left(3x^2\right)\right)$

Step-by-step Solution

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sinh
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asinh
acosh
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Solution

Formulas

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Final answer to the problem

$\frac{-2\mathrm{csch}\left(\ln\left(3x^2\right)\right)^2}{x}$
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Step-by-step Solution

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Learn how to solve power rule for derivatives problems step by step online. Find the derivative of coth(ln(3x^2)). Taking the derivative of hyperbolic cotangent. 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}. Multiplying the fraction by -1. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.

Final answer to the problem

$\frac{-2\mathrm{csch}\left(\ln\left(3x^2\right)\right)^2}{x}$

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Function Plot

Plotting: $\frac{-2\mathrm{csch}\left(\ln\left(3x^2\right)\right)^2}{x}$

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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
D□x
∫
∫◻
|◻|
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

How to improve your answer:

Similar Problems Solved

$\frac{d}{dx}\left(\ln\left(\mathrm{sech}\left(3x+8\right)\right)\right)$

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

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

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

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

$\frac{d}{dx}\arccos\left(\sqrt{1-x^2}\right)$

$\frac{d}{dx}\left(\sinh^2\left(3x\right)\right)$

Main Topic: Power Rule for Derivatives

The power rule is used to differentiate functions of the form f(x)=x^a, when a is a real number.

Used Formulas

See formulas (3)

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