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Popular >

derivative of sin^8(cos(2x))

Solution

derivative of

sin^{8} (cos (2 x))

Solution

- 16 sin^{7} (cos (2 x)) cos (cos (2 x)) sin (2 x)

Solution steps

\frac{d}{d x} (sin^{8} (cos (2 x)))

Apply the chain rule:

8 (sin (cos (2 x)))^{7} \frac{d}{d x} (sin (cos (2 x)))

= 8 (sin (cos (2 x)))^{7} \frac{d}{d x} (sin (cos (2 x)))

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

= 8 (sin (cos (2 x)))^{7} (- 2 cos (cos (2 x)) sin (2 x))

Simplify

= - 16 sin^{7} (cos (2 x)) cos (cos (2 x)) sin (2 x)

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Frequently Asked Questions (FAQ)

What is the derivative of sin^8(cos(2x)) ?
The derivative of sin^8(cos(2x)) is -16sin^7(cos(2x))cos(cos(2x))sin(2x)
What is the first derivative of sin^8(cos(2x)) ?
The first derivative of sin^8(cos(2x)) is -16sin^7(cos(2x))cos(cos(2x))sin(2x)