What is the derivative of cos^3(5x+1) ?

The derivative of cos^3(5x+1) is -15cos^2(5x+1)sin(5x+1)

What is the first derivative of cos^3(5x+1) ?

The first derivative of cos^3(5x+1) is -15cos^2(5x+1)sin(5x+1)

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\frac{d}{d x} (cos^{3} (5 x + 1))

- 15 cos^{2} (5 x + 1) sin (5 x + 1)

Solution steps

\frac{d}{d x} (cos^{3} (5 x + 1))

Apply the chain rule:

3 (cos (5 x + 1))^{2} \frac{d}{d x} (cos (5 x + 1))

= 3 (cos (5 x + 1))^{2} \frac{d}{d x} (cos (5 x + 1))

\frac{d}{d x} (cos (5 x + 1)) = - sin (5 x + 1) \cdot 5

= 3 (cos (5 x + 1))^{2} (- sin (5 x + 1) \cdot 5)

Simplify

= - 15 cos^{2} (5 x + 1) sin (5 x + 1)

What is the derivative of cos^3(5x+1) ?
The derivative of cos^3(5x+1) is -15cos^2(5x+1)sin(5x+1)
What is the first derivative of cos^3(5x+1) ?
The first derivative of cos^3(5x+1) is -15cos^2(5x+1)sin(5x+1)