What is the derivative of y=sin^4(x) ?

The derivative of y=sin^4(x) is 4sin^3(x)cos(x)

What is the first derivative of y=sin^4(x) ?

The first derivative of y=sin^4(x) is 4sin^3(x)cos(x)

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derivative of

y = sin^{4} (x)

4 sin^{3} (x) cos (x)

Solution steps

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

Apply the chain rule:

4 (sin (x))^{3} \frac{d}{d x} (sin (x))

= 4 (sin (x))^{3} \frac{d}{d x} (sin (x))

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

= 4 (sin (x))^{3} cos (x)

Simplify

= 4 sin^{3} (x) cos (x)

What is the derivative of y=sin^4(x) ?
The derivative of y=sin^4(x) is 4sin^3(x)cos(x)
What is the first derivative of y=sin^4(x) ?
The first derivative of y=sin^4(x) is 4sin^3(x)cos(x)