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

Step-by-step Solution

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Solution

Formulas

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Final answer to the problem

$-6\mathrm{csch}\left(6x\right)$
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Step-by-step Solution

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Learn how to solve basic differentiation rules problems step by step online. Find the derivative of ln(coth(3x)). 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 cotangent. Multiplying the fraction by -1. The derivative of the linear function times a constant, is equal to the constant.

Final answer to the problem

$-6\mathrm{csch}\left(6x\right)$

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Function Plot

Plotting: $-6\mathrm{csch}\left(6x\right)$

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0
a
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n
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x
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.
(◻)
+
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◻/◻
/
÷
◻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

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

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

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

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

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

Main Topic: Basic Differentiation Rules

Some differentiation rules are very easy to remember and use. These are the basic ones: constant rule, sum rule, product rule and quotient rule.

Used Formulas

See formulas (3)

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