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

The derivative of cos^3(x) is -3cos^2(x)sin(x)

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

The first derivative of cos^3(x) is -3cos^2(x)sin(x)

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derivative

- 3 cos^{2} (x) sin (x)

Solution steps

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

Apply the chain rule:

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

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

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

= 3 (cos (x))^{2} (- sin (x))

Simplify

= - 3 cos^{2} (x) sin (x)

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