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Find the derivative of $\ln\left(\mathrm{coth}\left(\frac{z}{2}\right)\right)$

Step-by-step Solution

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Solution

Formulas

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Final answer to the problem

$-\mathrm{csch}\left(z\right)$
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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(z/2)). 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 a function multiplied by a constant (\frac{1}{2}) is equal to the constant times the derivative of the function.

Final answer to the problem

$-\mathrm{csch}\left(z\right)$

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Function Plot

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

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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
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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