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Popular Calculus >

derivative of sin^3(cos(x))

Solution

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

Solution

- 3 sin^{2} (cos (x)) cos (cos (x)) sin (x)

Solution steps

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

Apply the chain rule:

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

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

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

= 3 (sin (cos (x)))^{2} (- cos (cos (x)) sin (x))

Simplify

= - 3 sin^{2} (cos (x)) cos (cos (x)) sin (x)

Graph

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\frac{d ^{2} y}{d x ^{2}} = \frac{( 6 x ^{5} )}{5} - 3 x

derivative of y=(x^2+1)/(x+1)

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x \to 0 lim (\frac{4}{3 + e ^{\frac{1}{x}}})

derivative of sin(2x+3y)

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

Frequently Asked Questions (FAQ)

What is the derivative of sin^3(cos(x)) ?
The derivative of sin^3(cos(x)) is -3sin^2(cos(x))cos(cos(x))sin(x)
What is the first derivative of sin^3(cos(x)) ?
The first derivative of sin^3(cos(x)) is -3sin^2(cos(x))cos(cos(x))sin(x)