What is the derivative of sin^6(x) ?

The derivative of sin^6(x) is 6sin^5(x)cos(x)

What is the first derivative of sin^6(x) ?

The first derivative of sin^6(x) is 6sin^5(x)cos(x)

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derivative of

sin^{6} (x)

6 sin^{5} (x) cos (x)

Solution steps

\frac{d}{d x} (sin^{6} (x))

Apply the chain rule:

6 (sin (x))^{5} \frac{d}{d x} (sin (x))

= 6 (sin (x))^{5} \frac{d}{d x} (sin (x))

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

= 6 (sin (x))^{5} cos (x)

Simplify

= 6 sin^{5} (x) cos (x)

What is the derivative of sin^6(x) ?
The derivative of sin^6(x) is 6sin^5(x)cos(x)
What is the first derivative of sin^6(x) ?
The first derivative of sin^6(x) is 6sin^5(x)cos(x)