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Popular >

derivative of e^{-x}(2-x)

Solution

\frac{d}{d x} (e^{- x} (2 - x))

Solution

e^{- x} x - 3 e^{- x}

Solution steps

\frac{d}{d x} (e^{- x} (2 - x))

Apply the Product Rule:

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

f = e^{- x}, g = 2 - x

= \frac{d}{d x} (e^{- x}) (2 - x) + \frac{d}{d x} (2 - x) e^{- x}

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

\frac{d}{d x} (2 - x) = - 1

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

Simplify

(- e^{- x}) (2 - x) + (- 1) e^{- x} : e^{- x} x - 3 e^{- x}

= e^{- x} x - 3 e^{- x}

Popular Examples

derivative of 39e^{1/x}

\frac{d}{d x} (39 e^{\frac{1}{x}})

derivative of e^x(2x^2+x-8)

\frac{d}{d x} (e^{x} (2 x^{2} + x - 8))

integral of-4x^4+8x^3

\int - 4 x^{4} + 8 x^{3} d x

integral of (2x-3)/(x^2+2x-17)

\int \frac{2 x - 3}{x ^{2} + 2 x - 17} d x

y^{1/2}(dy)/(dx)+y^{3/2}=1,y(0)=16

y^{\frac{1}{2}} \frac{d y}{d x} + y^{\frac{3}{2}} = 1, y (0) = 16

Frequently Asked Questions (FAQ)

What is the derivative of e^{-x}(2-x) ?
The derivative of e^{-x}(2-x) is e^{-x}x-3e^{-x}
What is the first derivative of e^{-x}(2-x) ?
The first derivative of e^{-x}(2-x) is e^{-x}x-3e^{-x}