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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

Popular Examples

limit as x approaches 3 of (1-2x)/(x-3)

x \to 3 lim (\frac{1 - 2 x}{x - 3})

derivative of f(x)=2x+1 derivative of

f (x) = 2 x + 1

(dy)/(dx)-y=e^{3x}

\frac{d y}{d x} - y = e^{3 x}

tangent of y=x^3-3x+2,(3,20)tangent of

y = x^{3} - 3 x + 2, (3, 20)

integral of (x-1)/(x^2-9)

\int \frac{x - 1}{x ^{2} - 9} d x

Frequently Asked Questions (FAQ)

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