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Popular >

derivative of Axe^{-2x}

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

= A \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}

= A (\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}

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

Simplify

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

Popular Examples

derivative of (2x-x^2/(3x^2+2))

\frac{d}{d x} (\frac{2 x - x ^{2}}{3 x ^{2} + 2})

(\partial)/(\partial x)(x/(x^7-y^4))

\frac{\partial}{\partial x} (\frac{x}{x ^{7} - y ^{4}})

derivative of (7x^2/(x^3))

\frac{d}{d x} (\frac{7 x ^{2}}{x ^{3}})

limit as x approaches 0 of (1+x)^{7/x}

x \to 0 lim ((1 + x)^{\frac{7}{x}})

k((dx)/(dt))=x+15

k (\frac{d x}{d t}) = x + 15

Frequently Asked Questions (FAQ)

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