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derivative of cos^2(sin(4x))

Solution

\frac{d}{d x} (cos^{2} (sin (4 x)))

Solution

- 8 cos (sin (4 x)) sin (sin (4 x)) cos (4 x)

Solution steps

\frac{d}{d x} (cos^{2} (sin (4 x)))

Apply the chain rule:

2 cos (sin (4 x)) \frac{d}{d x} (cos (sin (4 x)))

= 2 cos (sin (4 x)) \frac{d}{d x} (cos (sin (4 x)))

\frac{d}{d x} (cos (sin (4 x))) = - sin (sin (4 x)) cos (4 x) \cdot 4

= 2 cos (sin (4 x)) (- sin (sin (4 x)) cos (4 x) \cdot 4)

Simplify

= - 8 cos (sin (4 x)) sin (sin (4 x)) cos (4 x)

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Frequently Asked Questions (FAQ)

What is the derivative of cos^2(sin(4x)) ?
The derivative of cos^2(sin(4x)) is -8cos(sin(4x))sin(sin(4x))cos(4x)
What is the first derivative of cos^2(sin(4x)) ?
The first derivative of cos^2(sin(4x)) is -8cos(sin(4x))sin(sin(4x))cos(4x)