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Find the derivative of $\left(\cos\left(3x-1\right)^4\right)^3$

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 Final answer to the problem

$-36\cos\left(3x-1\right)^{11}\sin\left(3x-1\right)$
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 Step-by-step Solution 

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Simplify the derivative by applying the properties of logarithms

$\frac{d}{dx}\left(\cos\left(3x-1\right)^{12}\right)$

Learn how to solve limits of exponential functions problems step by step online.

$\frac{d}{dx}\left(\cos\left(3x-1\right)^{12}\right)$

Learn how to solve limits of exponential functions problems step by step online. Find the derivative of cos(3x-1)^4^3. Simplify the derivative by applying the properties of logarithms. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. 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). The derivative of a sum of two or more functions is the sum of the derivatives of each function.

 Final answer to the problem

$-36\cos\left(3x-1\right)^{11}\sin\left(3x-1\right)$

 Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Find the derivativeFind derivative of cos(3x-1)^4^3 using the product ruleFind derivative of cos(3x-1)^4^3 using the quotient ruleFind derivative of cos(3x-1)^4^3 using logarithmic differentiationFind derivative of cos(3x-1)^4^3 using the definition

SnapXam A2

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4
5
6
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

 Main Topic: Limits of Exponential Functions

Those are limits of expressions of the form f(x)^g(x).