What is the derivative of sin^5(2x) ?

The derivative of sin^5(2x) is 10sin^4(2x)cos(2x)

What is the first derivative of sin^5(2x) ?

The first derivative of sin^5(2x) is 10sin^4(2x)cos(2x)

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\frac{d}{d x} (sin^{5} (2 x))

10 sin^{4} (2 x) cos (2 x)

Solution steps

\frac{d}{d x} (sin^{5} (2 x))

Apply the chain rule:

5 (sin (2 x))^{4} \frac{d}{d x} (sin (2 x))

= 5 (sin (2 x))^{4} \frac{d}{d x} (sin (2 x))

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

= 5 (sin (2 x))^{4} cos (2 x) \cdot 2

Simplify

= 10 sin^{4} (2 x) cos (2 x)

What is the derivative of sin^5(2x) ?
The derivative of sin^5(2x) is 10sin^4(2x)cos(2x)
What is the first derivative of sin^5(2x) ?
The first derivative of sin^5(2x) is 10sin^4(2x)cos(2x)