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Popular >

derivative of cos(e^{-5x^2})

Solution

\frac{d}{d x} (cos (e^{- 5 x^{2}}))

Solution

10 e^{- 5 x^{2}} x sin (e^{- 5 x^{2}})

Solution steps

\frac{d}{d x} (cos (e^{- 5 x^{2}}))

Apply the chain rule:

- sin (e^{- 5 x^{2}}) \frac{d}{d x} (e^{- 5 x^{2}})

= - sin (e^{- 5 x^{2}}) \frac{d}{d x} (e^{- 5 x^{2}})

\frac{d}{d x} (e^{- 5 x^{2}}) = - 10 e^{- 5 x^{2}} x

= - sin (e^{- 5 x^{2}}) (- 10 e^{- 5 x^{2}} x)

Simplify

= 10 e^{- 5 x^{2}} x sin (e^{- 5 x^{2}})

Graph

Popular Examples

limit as x approaches 0 of (1-5x)^{5/x}

x \to 0 lim ((1 - 5 x)^{\frac{5}{x}})

integral of cos(ax)

\int cos (a x) d x

(d^2)/(dx^2)(5xcos(x^2))

\frac{d ^{2}}{d x ^{2}} (5 x cos (x^{2}))

integral of (3-2x)^5

\int (3 - 2 x)^{5} d x

(\partial)/(\partial x)(e^{(x+y)}-1)

\frac{\partial}{\partial x} (e^{(x + y)} - 1)

Frequently Asked Questions (FAQ)

What is the derivative of cos(e^{-5x^2}) ?
The derivative of cos(e^{-5x^2}) is 10e^{-5x^2}xsin(e^{-5x^2})
What is the first derivative of cos(e^{-5x^2}) ?
The first derivative of cos(e^{-5x^2}) is 10e^{-5x^2}xsin(e^{-5x^2})