What is the derivative of sin^4(6x^2) ?

The derivative of sin^4(6x^2) is 48xsin^3(6x^2)cos(6x^2)

What is the first derivative of sin^4(6x^2) ?

The first derivative of sin^4(6x^2) is 48xsin^3(6x^2)cos(6x^2)

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derivative of

sin^{4} (6 x^{2})

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

Solution steps

\frac{d}{d x} (sin^{4} (6 x^{2}))

Apply the chain rule:

4 (sin (6 x^{2}))^{3} \frac{d}{d x} (sin (6 x^{2}))

= 4 (sin (6 x^{2}))^{3} \frac{d}{d x} (sin (6 x^{2}))

\frac{d}{d x} (sin (6 x^{2})) = cos (6 x^{2}) \cdot 12 x

= 4 (sin (6 x^{2}))^{3} cos (6 x^{2}) \cdot 12 x

Simplify

= 48 x sin^{3} (6 x^{2}) cos (6 x^{2})

What is the derivative of sin^4(6x^2) ?
The derivative of sin^4(6x^2) is 48xsin^3(6x^2)cos(6x^2)
What is the first derivative of sin^4(6x^2) ?
The first derivative of sin^4(6x^2) is 48xsin^3(6x^2)cos(6x^2)