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Popular >

derivative of cos(x^{-5})

Solution

\frac{d}{d x} (cos (x^{- 5}))

Solution

\frac{5 sin ( \frac{1}{x ^{5}} )}{x ^{6}}

Solution steps

\frac{d}{d x} (cos (x^{- 5}))

Apply the chain rule:

- sin (x^{- 5}) \frac{d}{d x} (x^{- 5})

= - sin (x^{- 5}) \frac{d}{d x} (x^{- 5})

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

= - sin (x^{- 5}) (- \frac{5}{x ^{6}})

Simplify

- sin (x^{- 5}) (- \frac{5}{x ^{6}}) : \frac{5 sin ( \frac{1}{x ^{5}} )}{x ^{6}}

= \frac{5 sin ( \frac{1}{x ^{5}} )}{x ^{6}}

Popular Examples

integral of (2sin(θ)-csc(θ))^2

\int (2 sin (θ) - csc (θ))^{2} d θ

derivative of y=(4x-5)2 derivative of

y = (4 x - 5) 2

(x + \frac{9}{x})^{^{'}}

integral of 7cot^4(5t)

\int 7 cot^{4} (5 t) d t

integral from-1 to 1 of 1-x^4

\int_{- 1}^{1} 1 - x^{4} d x

Frequently Asked Questions (FAQ)

What is the derivative of cos(x^{-5}) ?
The derivative of cos(x^{-5}) is (5sin(1/(x^5)))/(x^6)
What is the first derivative of cos(x^{-5}) ?
The first derivative of cos(x^{-5}) is (5sin(1/(x^5)))/(x^6)