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Popular >

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

Solution

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

Solution

e^{- x} x

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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

Simplify

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

= e^{- x} x

Graph

Popular Examples

integral of (4x^3-2x+1)/x

\int \frac{4 x ^{3} - 2 x + 1}{x} d x

tangent of y=3x^3-x^2+1,(2,21)tangent of

y = 3 x^{3} - x^{2} + 1, (2, 21)

limit as x approaches infinity of 2x^2+1

x \to \infty lim (2 x^{2} + 1)

derivative of e^x+e

\frac{d}{d x} (e^{x} + e)

integral of (sin^2(x))/(cos^3(x))

\int \frac{sin ^{2} ( x )}{cos ^{3} ( x )} d x

Frequently Asked Questions (FAQ)

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