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Popular >

derivative of-2xe^{-2x}

Solution

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

Solution

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

Popular Examples

integral of (x^2+x-1)/(x^3+2x^2+x)

\int \frac{x ^{2} + x - 1}{x ^{3} + 2 x ^{2} + x} d x

integral of 1/(sqrt(x^2+y^2))

\int \frac{1}{x ^{2} + y ^{2}} d x

inverse oflaplace 9/(s^2+9s+9)*1/s inverse laplace

\frac{9}{s ^{2} + 9 s + 9} \cdot \frac{1}{s}

tangent of f(x)=x^4+9x^2-x,\at x=1 tangent of

f (x) = x^{4} + 9 x^{2} - x, at x = 1

sum from n=3 to infinity of (4/7)^n

n = 3 \sum \infty (\frac{4}{7})^{n}

Frequently Asked Questions (FAQ)

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