What is the derivative of sin^{23}(x) ?

The derivative of sin^{23}(x) is 23sin^{22}(x)cos(x)

What is the first derivative of sin^{23}(x) ?

The first derivative of sin^{23}(x) is 23sin^{22}(x)cos(x)

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derivative of

sin^{23} (x)

23 sin^{22} (x) cos (x)

Solution steps

\frac{d}{d x} (sin^{23} (x))

Apply the chain rule:

23 (sin (x))^{22} \frac{d}{d x} (sin (x))

= 23 (sin (x))^{22} \frac{d}{d x} (sin (x))

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

= 23 (sin (x))^{22} cos (x)

Simplify

= 23 sin^{22} (x) cos (x)

What is the derivative of sin^{23}(x) ?
The derivative of sin^{23}(x) is 23sin^{22}(x)cos(x)
What is the first derivative of sin^{23}(x) ?
The first derivative of sin^{23}(x) is 23sin^{22}(x)cos(x)