What is the derivative of sin^5(3x) ?

The derivative of sin^5(3x) is 15sin^4(3x)cos(3x)

What is the first derivative of sin^5(3x) ?

The first derivative of sin^5(3x) is 15sin^4(3x)cos(3x)

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\frac{d}{d x} (sin^{5} (3 x))

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

Solution steps

\frac{d}{d x} (sin^{5} (3 x))

Apply the chain rule:

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

= 5 (sin (3 x))^{4} \frac{d}{d x} (sin (3 x))

\frac{d}{d x} (sin (3 x)) = cos (3 x) \cdot 3

= 5 (sin (3 x))^{4} cos (3 x) \cdot 3

Simplify

= 15 sin^{4} (3 x) cos (3 x)

What is the derivative of sin^5(3x) ?
The derivative of sin^5(3x) is 15sin^4(3x)cos(3x)
What is the first derivative of sin^5(3x) ?
The first derivative of sin^5(3x) is 15sin^4(3x)cos(3x)