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Popular >

derivative of (1-xe^{-x})

Solution

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

Solution

- 2 e^{- x} + e^{- x} x

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 1 - x, g = e^{- x}

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

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

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

= (- 1) e^{- x} + (- e^{- x}) (1 - x)

Simplify

(- 1) e^{- x} + (- e^{- x}) (1 - x) : - 2 e^{- x} + e^{- x} x

= - 2 e^{- x} + e^{- x} x

Graph

Popular Examples

limit as x approaches 0 of (4sin(3x))/(2tan(5x))

x \to 0 lim (\frac{4 sin ( 3 x )}{2 tan ( 5 x )})

limit as x approaches (infinity) of (ln(x))/(sqrt(x))

x \to (\infty) lim (\frac{ln ( x )}{x})

limit as x approaches 1 of ((x^2))/(x-1)

x \to 1 lim (\frac{( x ^{2} )}{x - 1})

integral from 0 to 1 of (3x^2)/(1+x^3)

\int_{0}^{1} \frac{3 x ^{2}}{1 + x ^{3}} d x

x^2y^{''}-3xy^'+5y=0

x^{2} y^{^{''}} - 3 x y^{^{'}} + 5 y = 0

Frequently Asked Questions (FAQ)

What is the derivative of (1-xe^{-x}) ?
The derivative of (1-xe^{-x}) is -2e^{-x}+e^{-x}x
What is the first derivative of (1-xe^{-x}) ?
The first derivative of (1-xe^{-x}) is -2e^{-x}+e^{-x}x