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Popular >

derivative of cos(x^{-3})

Solution

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

Solution

\frac{3 sin ( \frac{1}{x ^{3}} )}{x ^{4}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{- 3}) = - \frac{3}{x ^{4}}

= - sin (x^{- 3}) (- \frac{3}{x ^{4}})

Simplify

- sin (x^{- 3}) (- \frac{3}{x ^{4}}) : \frac{3 sin ( \frac{1}{x ^{3}} )}{x ^{4}}

= \frac{3 sin ( \frac{1}{x ^{3}} )}{x ^{4}}

Popular Examples

slope ofintercept (-4,-4),(2,5)slope intercept

(- 4, - 4), (2, 5)

area f(x)=x,g(x)=sqrt(x)area

f (x) = x, g (x) = x

f^'(x)=(9x-2)/(8x+7)

f^{^{'}} (x) = \frac{9 x - 2}{8 x + 7}

derivative of axe^{-2x}

\frac{d}{d x} (a x e^{- 2 x})

(dy)/(dx)=(x+1)/(e^{3y+9)}

\frac{d y}{d x} = \frac{x + 1}{e ^{3 y + 9}}

Frequently Asked Questions (FAQ)

What is the derivative of cos(x^{-3}) ?
The derivative of cos(x^{-3}) is (3sin(1/(x^3)))/(x^4)
What is the first derivative of cos(x^{-3}) ?
The first derivative of cos(x^{-3}) is (3sin(1/(x^3)))/(x^4)