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

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Final answer to the problem

$-3\tan\left(3x\right)$
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Step-by-step Solution

How should I solve this problem?

  • Find the derivative using the quotient rule
  • Find the derivative using the definition
  • Find the derivative using the product rule
  • Find the derivative using logarithmic differentiation
  • Find the derivative
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
  • Load more...
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The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$

$\frac{1}{\cos\left(3x\right)}\frac{d}{dx}\left(\cos\left(3x\right)\right)$

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$\frac{1}{\cos\left(3x\right)}\frac{d}{dx}\left(\cos\left(3x\right)\right)$

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Learn how to solve problems step by step online. Find the derivative using the quotient rule d/dx(ln(cos(3x))). The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x). Multiplying the fraction by -1. The derivative of the linear function times a constant, is equal to the constant.

Final answer to the problem

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

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

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7
8
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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