What is the derivative of sin^8(x) ?

The derivative of sin^8(x) is 8sin^7(x)cos(x)

What is the first derivative of sin^8(x) ?

The first derivative of sin^8(x) is 8sin^7(x)cos(x)

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derivative of

sin^{8} (x)

8 sin^{7} (x) cos (x)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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