en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of cos^3(e^{-x})

Solution

\frac{d}{d x} (cos^{3} (e^{- x}))

Solution

3 e^{- x} cos^{2} (e^{- x}) sin (e^{- x})

Solution steps

\frac{d}{d x} (cos^{3} (e^{- x}))

Apply the chain rule:

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

= 3 (cos (e^{- x}))^{2} \frac{d}{d x} (cos (e^{- x}))

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

= 3 (cos (e^{- x}))^{2} e^{- x} sin (e^{- x})

Simplify

= 3 e^{- x} cos^{2} (e^{- x}) sin (e^{- x})

Popular Examples

integral of cos((mpix)/3)

\int cos (\frac{mπ x}{3}) d x

(\partial)/(\partial y)(2ycos(x))

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

y^{''}+2y^'+2y=sin(sqrt(2)x)

y^{^{''}} + 2 y^{^{'}} + 2 y = sin (2 x)

limit as x approaches 0+of e^{-5/x}

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

integral of 1/(sqrt(-x^2+14x+50))

\int \frac{1}{- x ^{2} + 14 x + 50} d x

Frequently Asked Questions (FAQ)

What is the derivative of cos^3(e^{-x}) ?
The derivative of cos^3(e^{-x}) is 3e^{-x}cos^2(e^{-x})sin(e^{-x})
What is the first derivative of cos^3(e^{-x}) ?
The first derivative of cos^3(e^{-x}) is 3e^{-x}cos^2(e^{-x})sin(e^{-x})