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Popular >

derivative of cos(x^{-7})

Solution

derivative of

cos (x^{- 7})

Solution

\frac{7 sin ( \frac{1}{x ^{7}} )}{x ^{8}}

Solution steps

\frac{d}{d x} (cos (x^{- 7}))

Apply the chain rule:

- sin (x^{- 7}) \frac{d}{d x} (x^{- 7})

= - sin (x^{- 7}) \frac{d}{d x} (x^{- 7})

\frac{d}{d x} (x^{- 7}) = - \frac{7}{x ^{8}}

= - sin (x^{- 7}) (- \frac{7}{x ^{8}})

Simplify

- sin (x^{- 7}) (- \frac{7}{x ^{8}}) : \frac{7 sin ( \frac{1}{x ^{7}} )}{x ^{8}}

= \frac{7 sin ( \frac{1}{x ^{7}} )}{x ^{8}}

Popular Examples

y^'=(3x+2y)/(3x+2y+2)

y^{^{'}} = \frac{3 x + 2 y}{3 x + 2 y + 2}

ydy=(2x)/((1+x^2))dx,y(0)=2

y d y = \frac{2 x}{( 1 + x ^{2} )} d x, y (0) = 2

(\partial)/(\partial y)(3x^{3y})

\frac{\partial}{\partial y} (3 x^{3 y})

integral of (5x-4)^2

\int (5 x - 4)^{2} d x

derivative of f(x)=(3x+5)^3 derivative of

f (x) = (3 x + 5)^{3}

Frequently Asked Questions (FAQ)

What is the derivative of cos(x^{-7}) ?
The derivative of cos(x^{-7}) is (7sin(1/(x^7)))/(x^8)
What is the first derivative of cos(x^{-7}) ?
The first derivative of cos(x^{-7}) is (7sin(1/(x^7)))/(x^8)