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Popular >

derivative of sin^4(cos(8x))

Solution

\frac{d}{d x} (sin^{4} (cos (8 x)))

Solution

- 32 sin^{3} (cos (8 x)) cos (cos (8 x)) sin (8 x)

Solution steps

\frac{d}{d x} (sin^{4} (cos (8 x)))

Apply the chain rule:

4 (sin (cos (8 x)))^{3} \frac{d}{d x} (sin (cos (8 x)))

= 4 (sin (cos (8 x)))^{3} \frac{d}{d x} (sin (cos (8 x)))

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

= 4 (sin (cos (8 x)))^{3} (- 8 cos (cos (8 x)) sin (8 x))

Simplify

= - 32 sin^{3} (cos (8 x)) cos (cos (8 x)) sin (8 x)

Popular Examples

limit as x approaches 4 of x^4-5x^2+2

x \to 4 lim (x^{4} - 5 x^{2} + 2)

area f(x)= 1/x ,[1,2]area

f (x) = \frac{1}{x}, [1, 2]

integral from-5 to 0 of 2^{1-x}

\int_{- 5}^{0} 2^{1 - x} d x

tangent of y=(6x)/(x^2+1)tangent of

y = \frac{6 x}{x ^{2} + 1}

(\partial)/(\partial x)(xsin(2y))

\frac{\partial}{\partial x} (x sin (2 y))

Frequently Asked Questions (FAQ)

What is the derivative of sin^4(cos(8x)) ?
The derivative of sin^4(cos(8x)) is -32sin^3(cos(8x))cos(cos(8x))sin(8x)
What is the first derivative of sin^4(cos(8x)) ?
The first derivative of sin^4(cos(8x)) is -32sin^3(cos(8x))cos(cos(8x))sin(8x)