What is the derivative of cos^3(2x) ?

The derivative of cos^3(2x) is -6cos^2(2x)sin(2x)

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

The first derivative of cos^3(2x) is -6cos^2(2x)sin(2x)

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (cos (2 x)) = - sin (2 x) \cdot 2

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

Simplify

= - 6 cos^{2} (2 x) sin (2 x)

What is the derivative of cos^3(2x) ?
The derivative of cos^3(2x) is -6cos^2(2x)sin(2x)
What is the first derivative of cos^3(2x) ?
The first derivative of cos^3(2x) is -6cos^2(2x)sin(2x)