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Popular >

derivative of c_{1}e^{-2x}+c_{2}xe^{-2x}

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Popular Examples

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

integral of 1/((5-4x-x^2)^{5/2)}

\int \frac{1}{( 5 - 4 x - x ^{2} ) ^{\frac{5}{2}}} d x

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\int \frac{1}{cos ( x ) + sin ( x )} d x

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\frac{5}{( s + 2 ) ^{4}}

derivative of a(x+1(x-{r}(x)))

\frac{d}{d x} (a (x + 1) (x - r (x)))

Frequently Asked Questions (FAQ)

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