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Popular >

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

Solution

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

Solution

25 e^{- 5 x^{5}} x^{4} sin (e^{- 5 x^{5}})

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (e^{- 5 x^{5}}) = - 25 e^{- 5 x^{5}} x^{4}

= - sin (e^{- 5 x^{5}}) (- 25 e^{- 5 x^{5}} x^{4})

Simplify

= 25 e^{- 5 x^{5}} x^{4} sin (e^{- 5 x^{5}})

Popular Examples

integral of (sqrt(8+tan(x)))/(1-sin^2(x))

\int \frac{8 + tan ( x )}{1 - sin ^{2} ( x )} d x

integral of 4/(t^2)

\int \frac{4}{t ^{2}} d t

tangent of 22x^3 tangent of

22 x^{3}

(\partial)/(\partial x)(sqrt(y+(cos^2(x))))

\frac{\partial}{\partial x} (y + (cos^{2} (x)))

limit as x approaches 2 of sin(x)

x \to 2 lim (sin (x))

Frequently Asked Questions (FAQ)

What is the derivative of cos(e^{-5x^5}) ?
The derivative of cos(e^{-5x^5}) is 25e^{-5x^5}x^4sin(e^{-5x^5})
What is the first derivative of cos(e^{-5x^5}) ?
The first derivative of cos(e^{-5x^5}) is 25e^{-5x^5}x^4sin(e^{-5x^5})