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Popular >

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

Solution

derivative of

e^{- x + 1} - x \cdot e^{- x + 1}

Solution

- 2 e^{- x + 1} + e^{- x + 1} x

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= - 2 e^{- x + 1} + e^{- x + 1} x

Popular Examples

integral of 14sin^3(x)cos^2(x)

\int 14 sin^{3} (x) cos^{2} (x) d x

integral of (5sqrt(x))/(x^3+1)

\int \frac{5 x}{x ^{3} + 1} d x

y^'+2ty^2=0,y(1)= 1/5

y^{^{'}} + 2 t y^{2} = 0, y (1) = \frac{1}{5}

limit as x approaches 0+of 1/(2x)

x \to 0 + lim (\frac{1}{2 x})

integral of (cos(4x))

\int (cos (4 x)) d x

Frequently Asked Questions (FAQ)

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