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Popular >

derivative of cos(x^{-4})

Solution

\frac{d}{d x} (cos (x^{- 4}))

Solution

\frac{4 sin ( \frac{1}{x ^{4}} )}{x ^{5}}

Solution steps

\frac{d}{d x} (cos (x^{- 4}))

Apply the chain rule:

- sin (x^{- 4}) \frac{d}{d x} (x^{- 4})

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

\frac{d}{d x} (x^{- 4}) = - \frac{4}{x ^{5}}

= - sin (x^{- 4}) (- \frac{4}{x ^{5}})

Simplify

- sin (x^{- 4}) (- \frac{4}{x ^{5}}) : \frac{4 sin ( \frac{1}{x ^{4}} )}{x ^{5}}

= \frac{4 sin ( \frac{1}{x ^{4}} )}{x ^{5}}

Graph

Popular Examples

limit as x approaches 2 of 5/(x-2)

x \to 2 lim (\frac{5}{x - 2})

slope of (3,-3),(5,-6)slope

(3, - 3), (5, - 6)

y^{''}-2y^'+y=xe^xln(x)

y^{^{''}} - 2 y^{^{'}} + y = x e^{x} ln (x)

limit as x approaches 3 of 3x^3-5x^2+x-8

x \to 3 lim (3 x^{3} - 5 x^{2} + x - 8)

(dy}{dx}=\frac{(xy)^2)/8+y^2

\frac{d y}{d x} = \frac{( x y ) ^{2}}{8} + y^{2}

Frequently Asked Questions (FAQ)

What is the derivative of cos(x^{-4}) ?
The derivative of cos(x^{-4}) is (4sin(1/(x^4)))/(x^5)
What is the first derivative of cos(x^{-4}) ?
The first derivative of cos(x^{-4}) is (4sin(1/(x^4)))/(x^5)