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

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

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

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

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derivative of

sin^{4} (3 x^{2})

24 x sin^{3} (3 x^{2}) cos (3 x^{2})

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (sin (3 x^{2})) = cos (3 x^{2}) \cdot 6 x

= 4 (sin (3 x^{2}))^{3} cos (3 x^{2}) \cdot 6 x

Simplify

= 24 x sin^{3} (3 x^{2}) cos (3 x^{2})

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