What is the derivative of sin^3(2x-3) ?

The derivative of sin^3(2x-3) is 6sin^2(2x-3)cos(2x-3)

What is the first derivative of sin^3(2x-3) ?

The first derivative of sin^3(2x-3) is 6sin^2(2x-3)cos(2x-3)

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\frac{d}{d x} (sin^{3} (2 x - 3))

6 sin^{2} (2 x - 3) cos (2 x - 3)

Solution steps

\frac{d}{d x} (sin^{3} (2 x - 3))

Apply the chain rule:

3 (sin (2 x - 3))^{2} \frac{d}{d x} (sin (2 x - 3))

= 3 (sin (2 x - 3))^{2} \frac{d}{d x} (sin (2 x - 3))

\frac{d}{d x} (sin (2 x - 3)) = cos (2 x - 3) \cdot 2

= 3 (sin (2 x - 3))^{2} cos (2 x - 3) \cdot 2

Simplify

= 6 sin^{2} (2 x - 3) cos (2 x - 3)

What is the derivative of sin^3(2x-3) ?
The derivative of sin^3(2x-3) is 6sin^2(2x-3)cos(2x-3)
What is the first derivative of sin^3(2x-3) ?
The first derivative of sin^3(2x-3) is 6sin^2(2x-3)cos(2x-3)