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Find the derivative using logarithmic differentiation method $\frac{d}{dx}\left(x^{4\cos\left(x\right)}\right)$

Used Formulas

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Solution

Formulas

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Basic Derivatives

$\frac{d}{dx}\left(cx\right)=c\frac{d}{dx}\left(x\right)$
· 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 natural logarithm
$\frac{d}{dx}\left(\ln\left(x\right)\right)=\frac{1}{x}\frac{d}{dx}\left(x\right)$
· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$

Derivatives of trigonometric functions

· Derivative of the cosine function
$\frac{d}{dx}\left(\cos\left(\theta \right)\right)=-\sin\left(\theta \right)$

Function Plot

Plotting: $4\left(-x\sin\left(x\right)\ln\left(x\right)+\cos\left(x\right)\right)x^{\left(4\cos\left(x\right)-1\right)}$

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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

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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 (5)

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