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Popular >

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

Solution

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

Solution

4 e^{- 2 x} x - 4 e^{- 2 x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

- 2 e^{- 2 x} - 2 (- 2 e^{- 2 x} x + e^{- 2 x}) : 4 e^{- 2 x} x - 4 e^{- 2 x}

= 4 e^{- 2 x} x - 4 e^{- 2 x}

Popular Examples

d/(dt)(-1cos(t)+8sin(t))

\frac{d}{d t} (- 1 cos (t) + 8 sin (t))

integral from 0 to 1 of 4sqrt(x)-4x

\int_{0}^{1} 4 x - 4 x d x

integral of (x^5)/((3-x^6)^4)

\int \frac{x ^{5}}{( 3 - x ^{6} ) ^{4}} d x

y^{''}+7y^'+12y=0

y^{^{''}} + 7 y^{^{'}} + 12 y = 0

sum from n=5 to infinity of (n!)/(n^n)

n = 5 \sum \infty \frac{n !}{n ^{n}}

Frequently Asked Questions (FAQ)

What is the derivative of e^{-2x}-2e^{-2x}x ?
The derivative of e^{-2x}-2e^{-2x}x is 4e^{-2x}x-4e^{-2x}
What is the first derivative of e^{-2x}-2e^{-2x}x ?
The first derivative of e^{-2x}-2e^{-2x}x is 4e^{-2x}x-4e^{-2x}