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Popular >

derivative of sin^8(5x^2+8)

Solution

\frac{d}{d x} (sin^{8} (5 x^{2} + 8))

Solution

80 x sin^{7} (5 x^{2} + 8) cos (5 x^{2} + 8)

Solution steps

\frac{d}{d x} (sin^{8} (5 x^{2} + 8))

Apply the chain rule:

8 (sin (5 x^{2} + 8))^{7} \frac{d}{d x} (sin (5 x^{2} + 8))

= 8 (sin (5 x^{2} + 8))^{7} \frac{d}{d x} (sin (5 x^{2} + 8))

\frac{d}{d x} (sin (5 x^{2} + 8)) = cos (5 x^{2} + 8) \cdot 10 x

= 8 (sin (5 x^{2} + 8))^{7} cos (5 x^{2} + 8) \cdot 10 x

Simplify

= 80 x sin^{7} (5 x^{2} + 8) cos (5 x^{2} + 8)

Popular Examples

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\int \frac{e ^{13 x}}{( e ^{13 x} + 5 ) ^{4}} d x

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\frac{d y}{d x} - 0.11 y = 200

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Frequently Asked Questions (FAQ)

What is the derivative of sin^8(5x^2+8) ?
The derivative of sin^8(5x^2+8) is 80xsin^7(5x^2+8)cos(5x^2+8)
What is the first derivative of sin^8(5x^2+8) ?
The first derivative of sin^8(5x^2+8) is 80xsin^7(5x^2+8)cos(5x^2+8)