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Find the derivative using logarithmic differentiation method $\frac{d}{dx}\left(\frac{\left(x^5+3x\right)^4}{\cos\left(x\right)}\right)$

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Solution

Formulas

Videos

Basic Derivatives

· 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
$\frac{d}{dx}\left(x\right)=1$
· Sum Rule for Differentiation
$\frac{d}{dx}\left[f\left(x\right)+g\left(x\right)\right]=\frac{d}{dx}f\left(x\right) + \frac{d}{dx}g\left(x\right)$
$\frac{d}{dx}\left(cx\right)=c\frac{d}{dx}\left(x\right)$
· Power rule for derivatives
$\frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}$

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: $\left(\frac{20x^{4}+12}{x^5+3x}+\tan\left(x\right)\right)\frac{\left(x^5+3x\right)^4}{\cos\left(x\right)}$

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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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Main Topic: Logarithmic Differentiation

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

Used Formulas

6. See formulas

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