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

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Solution

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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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  • Find the derivative using the definition
  • Find the derivative using the product rule
  • Find the derivative using the quotient 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
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1

Simplify the derivative by applying the properties of logarithms

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

Learn how to solve differential calculus problems step by step online.

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

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Learn how to solve differential calculus 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

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

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Function Plot

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

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x
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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

How to improve your answer:

Similar Problems Solved

Find the derivative

$\frac{d}{dx}\left(x^2+y^2\right)$

$\frac{d}{dx}\left(\arctan\left(x-\sqrt{1+x^2}\right)\right)$

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$\frac{d}{dx}\arccos\left(\sqrt{1-x^2}\right)$

$\frac{d}{dx}\ln\left(x^2+1\right)$

$\frac{d}{dx}\left(\sin^2\left(x\right)\right)$

$\frac{d}{dx}\left(x\sqrt{x^2-1}\right)$

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.

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