What is the derivative of cos^5(3x) ?

The derivative of cos^5(3x) is -15cos^4(3x)sin(3x)

What is the first derivative of cos^5(3x) ?

The first derivative of cos^5(3x) is -15cos^4(3x)sin(3x)

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\frac{d}{d x} (cos^{5} (3 x))

- 15 cos^{4} (3 x) sin (3 x)

Solution steps

\frac{d}{d x} (cos^{5} (3 x))

Apply the chain rule:

5 (cos (3 x))^{4} \frac{d}{d x} (cos (3 x))

= 5 (cos (3 x))^{4} \frac{d}{d x} (cos (3 x))

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

= 5 (cos (3 x))^{4} (- sin (3 x) \cdot 3)

Simplify

= - 15 cos^{4} (3 x) sin (3 x)

What is the derivative of cos^5(3x) ?
The derivative of cos^5(3x) is -15cos^4(3x)sin(3x)
What is the first derivative of cos^5(3x) ?
The first derivative of cos^5(3x) is -15cos^4(3x)sin(3x)