en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(x)=x*e^{-x+1}

Solution

derivative of

f (x) = x \cdot e^{- x + 1}

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

Popular Examples

tangent of 4+5x^2-2x^3 tangent of

4 + 5 x^{2} - 2 x^{3}

derivative of (sin(x+cos(x))/(e^x))

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

limit as x approaches 5-of 8-x-x^2

x \to 5 - lim (8 - x - x^{2})

y^'=(x-2)/(y-2)

y^{^{'}} = \frac{x - 2}{y - 2}

(\partial)/(\partial x)(2x^2+3y^2+5z^2)

\frac{\partial}{\partial x} (2 x^{2} + 3 y^{2} + 5 z^{2})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=x*e^{-x+1} ?
The derivative of f(x)=x*e^{-x+1} is e^{-x+1}-e^{-x+1}x
What is the first derivative of f(x)=x*e^{-x+1} ?
The first derivative of f(x)=x*e^{-x+1} is e^{-x+1}-e^{-x+1}x