Find the derivative using the quotient rule $\frac{d}{dx}\left(\ln\left(\cos\left(3x\right)\right)\right)$

Used Formulas

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e
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ln
log
log
lim
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sin
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cot
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asin
acos
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acot
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sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Basic Derivatives

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

Derivatives of trigonometric functions

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

Function Plot

Plotting: $-3\tan\left(3x\right)$

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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
Dx
|◻|
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: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

Used Formulas

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