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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

Popular Examples

derivative of e^{3xy}

\frac{d}{d x} (e^{3 x y})

limit as h approaches 0 of ((f(h)(4+h)-f(4)))/h

h \to 0 lim (\frac{( f ( h ) ( 4 + h ) - f ( 4 ) )}{h})

(\partial)/(\partial x)(e^{-x}cos(y))

\frac{\partial}{\partial x} (e^{- x} cos (y))

slope of y=x^3 slope

y = x^{3}

x y^{^{'}} + x y = 1 - y

Frequently Asked Questions (FAQ)

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