What is the derivative of cos^2(5x) ?

The derivative of cos^2(5x) is -5sin(10x)

What is the first derivative of cos^2(5x) ?

The first derivative of cos^2(5x) is -5sin(10x)

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derivative of

cos^{2} (5 x)

- 5 sin (10 x)

Solution steps

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

Apply the chain rule:

2 cos (5 x) \frac{d}{d x} (cos (5 x))

= 2 cos (5 x) \frac{d}{d x} (cos (5 x))

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

= 2 cos (5 x) (- sin (5 x) \cdot 5)

Simplify

2 cos (5 x) (- sin (5 x) \cdot 5) : - 5 sin (10 x)

= - 5 sin (10 x)

What is the derivative of cos^2(5x) ?
The derivative of cos^2(5x) is -5sin(10x)
What is the first derivative of cos^2(5x) ?
The first derivative of cos^2(5x) is -5sin(10x)