What is the derivative of sin^3(4x^2-1) ?

The derivative of sin^3(4x^2-1) is 24xsin^2(4x^2-1)cos(4x^2-1)

What is the first derivative of sin^3(4x^2-1) ?

The first derivative of sin^3(4x^2-1) is 24xsin^2(4x^2-1)cos(4x^2-1)

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\frac{d}{d x} (sin^{3} (4 x^{2} - 1))

24 x sin^{2} (4 x^{2} - 1) cos (4 x^{2} - 1)

Solution steps

\frac{d}{d x} (sin^{3} (4 x^{2} - 1))

Apply the chain rule:

3 (sin (4 x^{2} - 1))^{2} \frac{d}{d x} (sin (4 x^{2} - 1))

= 3 (sin (4 x^{2} - 1))^{2} \frac{d}{d x} (sin (4 x^{2} - 1))

\frac{d}{d x} (sin (4 x^{2} - 1)) = cos (4 x^{2} - 1) \cdot 8 x

= 3 (sin (4 x^{2} - 1))^{2} cos (4 x^{2} - 1) \cdot 8 x

Simplify

= 24 x sin^{2} (4 x^{2} - 1) cos (4 x^{2} - 1)

What is the derivative of sin^3(4x^2-1) ?
The derivative of sin^3(4x^2-1) is 24xsin^2(4x^2-1)cos(4x^2-1)
What is the first derivative of sin^3(4x^2-1) ?
The first derivative of sin^3(4x^2-1) is 24xsin^2(4x^2-1)cos(4x^2-1)