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Find the derivative using logarithmic differentiation method $\frac{d}{dx}\left(x^{7\sin\left(x\right)}\right)$

Used Formulas

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Solution

Formulas

Videos

Basic Differentiation Rules

$\frac{d}{dx}\left(cx\right)=c\frac{d}{dx}\left(x\right)$
· 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 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 the sine function
$\frac{d}{dx}\left(\sin\left(\theta \right)\right)=\frac{d}{dx}\left(\theta \right)\cos\left(\theta \right)$

Function Plot

Plotting: $7\left(\cos\left(x\right)\ln\left(x\right)+\frac{\sin\left(x\right)}{x}\right)x^{7\sin\left(x\right)}$

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0
a
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d
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n
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y
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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

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Find the derivative

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Main Topic: Product Rule of differentiation

The product rule is a formula used to find the derivatives of products of two or more functions. It may be stated as $(f\cdot g)'=f'\cdot g+f\cdot g'$

Used Formulas

See formulas (5)

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