en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 1-e^{-x}-xe^{-x}

Solution

\frac{d}{d x} (1 - e^{- x} - x e^{- x})

Solution

e^{- x} x

Solution steps

\frac{d}{d x} (1 - e^{- x} - x e^{- x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (1) - \frac{d}{d x} (e^{- x}) - \frac{d}{d x} (x e^{- x})

\frac{d}{d x} (1) = 0

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

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

= 0 - (- e^{- x}) - (e^{- x} - e^{- x} x)

Simplify

0 - (- e^{- x}) - (e^{- x} - e^{- x} x) : e^{- x} x

= e^{- x} x

Popular Examples

ty^'=y-5t^2sin(3t),y(pi/3)=0

t y^{^{'}} = y - 5 t^{2} sin (3 t), y (\frac{π}{3}) = 0

(\partial)/(\partial x)(e^{2x}sin(y))

\frac{\partial}{\partial x} (e^{2 x} sin (y))

limit as x approaches 0 of cot(5x)

x \to 0 lim (cot (5 x))

(\partial)/(\partial x)(2y+3ysin(x))

\frac{\partial}{\partial x} (2 y + 3 y sin (x))

derivative of arcsin(x/(sqrt(1+x^2)))

\frac{d}{d x} (arcsin (\frac{x}{1 + x ^{2}}))

Frequently Asked Questions (FAQ)

What is the derivative of 1-e^{-x}-xe^{-x} ?
The derivative of 1-e^{-x}-xe^{-x} is e^{-x}x
What is the first derivative of 1-e^{-x}-xe^{-x} ?
The first derivative of 1-e^{-x}-xe^{-x} is e^{-x}x