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Popular >

derivative of sin^9(cos(8x))

Solution

\frac{d}{d x} (sin^{9} (cos (8 x)))

Solution

- 72 sin^{8} (cos (8 x)) cos (cos (8 x)) sin (8 x)

Solution steps

\frac{d}{d x} (sin^{9} (cos (8 x)))

Apply the chain rule:

9 (sin (cos (8 x)))^{8} \frac{d}{d x} (sin (cos (8 x)))

= 9 (sin (cos (8 x)))^{8} \frac{d}{d x} (sin (cos (8 x)))

\frac{d}{d x} (sin (cos (8 x))) = - 8 cos (cos (8 x)) sin (8 x)

= 9 (sin (cos (8 x)))^{8} (- 8 cos (cos (8 x)) sin (8 x))

Simplify

= - 72 sin^{8} (cos (8 x)) cos (cos (8 x)) sin (8 x)

Popular Examples

integral of (8x+15)ln(2x)

\int (8 x + 15) ln (2 x) d x

integral of t^2e^{-9t}

\int t^{2} e^{- 9 t} d t

integral from 1 to 4 of (3ln(x))/(x^2)

\int_{1}^{4} \frac{3 ln ( x )}{x ^{2}} d x

derivative of (x^4/9)

\frac{d}{d x} (\frac{x ^{4}}{9})

area y=2916sqrt(x),108x^2 area

y = 2916 x, 108 x^{2}

Frequently Asked Questions (FAQ)

What is the derivative of sin^9(cos(8x)) ?
The derivative of sin^9(cos(8x)) is -72sin^8(cos(8x))cos(cos(8x))sin(8x)
What is the first derivative of sin^9(cos(8x)) ?
The first derivative of sin^9(cos(8x)) is -72sin^8(cos(8x))cos(cos(8x))sin(8x)