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Popular >

derivative of (1-2xe^{-x})

Solution

\frac{d}{d x} ((1 - 2 x) e^{- x})

Solution

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

Solution steps

\frac{d}{d x} ((1 - 2 x) e^{- x})

Apply the Product Rule:

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

f = 1 - 2 x, g = e^{- x}

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

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

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

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

Simplify

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

= - 3 e^{- x} + 2 e^{- x} x

Popular Examples

(\partial)/(\partial x)(xln(ycos(x)))

\frac{\partial}{\partial x} (x ln (y cos (x)))

derivative of x^4-10x^2+9

\frac{d}{d x} (x^{4} - 10 x^{2} + 9)

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integral of (x+20)/(x^2+18x+85)

\int \frac{x + 20}{x ^{2} + 18 x + 85} d x

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

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

Frequently Asked Questions (FAQ)

What is the derivative of (1-2xe^{-x}) ?
The derivative of (1-2xe^{-x}) is -3e^{-x}+2e^{-x}x
What is the first derivative of (1-2xe^{-x}) ?
The first derivative of (1-2xe^{-x}) is -3e^{-x}+2e^{-x}x