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Popular >

derivative of cos(x^{-9})

Solution

derivative of

cos (x^{- 9})

Solution

\frac{9 sin ( \frac{1}{x ^{9}} )}{x ^{10}}

Solution steps

\frac{d}{d x} (cos (x^{- 9}))

Apply the chain rule:

- sin (x^{- 9}) \frac{d}{d x} (x^{- 9})

= - sin (x^{- 9}) \frac{d}{d x} (x^{- 9})

\frac{d}{d x} (x^{- 9}) = - \frac{9}{x ^{10}}

= - sin (x^{- 9}) (- \frac{9}{x ^{10}})

Simplify

- sin (x^{- 9}) (- \frac{9}{x ^{10}}) : \frac{9 sin ( \frac{1}{x ^{9}} )}{x ^{10}}

= \frac{9 sin ( \frac{1}{x ^{9}} )}{x ^{10}}

Popular Examples

derivative of 3-7/(2x^{1/8})

\frac{d}{d x} (3 - \frac{7}{2 x ^{\frac{1}{8}}})

area x^2+y^2=4,x^2+y^2=4x area

x^{2} + y^{2} = 4, x^{2} + y^{2} = 4 x

d/(dy)((y^{3/2})/5)

\frac{d}{d y} (\frac{y ^{\frac{3}{2}}}{5})

integral of ((x^2+1-2x)^{1/5})/(1-x)

\int \frac{( x ^{2} + 1 - 2 x ) ^{\frac{1}{5}}}{1 - x} d x

integral of (x^6)/(sqrt(1-x^{14))}

\int \frac{x ^{6}}{1 - x ^{14}} d x

Frequently Asked Questions (FAQ)

What is the derivative of cos(x^{-9}) ?
The derivative of cos(x^{-9}) is (9sin(1/(x^9)))/(x^{10)}
What is the first derivative of cos(x^{-9}) ?
The first derivative of cos(x^{-9}) is (9sin(1/(x^9)))/(x^{10)}