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Find the derivative using logarithmic differentiation method $\frac{d}{dx}\left(x^{\cot\left(x\right)}\right)$

Used Formulas

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Solution

Formulas

Videos

Basic Derivatives

· Product rule for derivatives
$\frac{d}{dx}\left(ab\right)=\frac{d}{dx}\left(a\right)b+a\frac{d}{dx}\left(b\right)$
· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$
· Derivative of the natural logarithm
$\frac{d}{dx}\left(\ln\left(x\right)\right)=\frac{1}{x}\frac{d}{dx}\left(x\right)$

Derivatives of trigonometric functions

· Derivative of cotangent function
$\frac{d}{dx}\left(\cot\left(\theta \right)\right)=-\frac{d}{dx}\left(\theta \right)\csc\left(\theta \right)^2$

Function Plot

Plotting: $\left(-\csc\left(x\right)^2\ln\left(x\right)+\frac{\cot\left(x\right)}{x}\right)x^{\cot\left(x\right)}$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
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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:

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Find the derivative

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

Main Topic: Logarithmic Differentiation

The logarithmic derivative of a function f(x) is defined by the formula f'(x)/f(x).

Used Formulas

See formulas (4)

Related Topics

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