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Popular >

derivative of sin^3(x^2+7)

Solution

\frac{d}{d x} (sin^{3} (x^{2} + 7))

Solution

6 x sin^{2} (x^{2} + 7) cos (x^{2} + 7)

Solution steps

\frac{d}{d x} (sin^{3} (x^{2} + 7))

Apply the chain rule:

3 (sin (x^{2} + 7))^{2} \frac{d}{d x} (sin (x^{2} + 7))

= 3 (sin (x^{2} + 7))^{2} \frac{d}{d x} (sin (x^{2} + 7))

\frac{d}{d x} (sin (x^{2} + 7)) = cos (x^{2} + 7) \cdot 2 x

= 3 (sin (x^{2} + 7))^{2} cos (x^{2} + 7) \cdot 2 x

Simplify

= 6 x sin^{2} (x^{2} + 7) cos (x^{2} + 7)

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Frequently Asked Questions (FAQ)

What is the derivative of sin^3(x^2+7) ?
The derivative of sin^3(x^2+7) is 6xsin^2(x^2+7)cos(x^2+7)
What is the first derivative of sin^3(x^2+7) ?
The first derivative of sin^3(x^2+7) is 6xsin^2(x^2+7)cos(x^2+7)