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Popular >

derivative of xe^{-4x}

Solution

\frac{d}{d x} (x e^{- 4 x})

Solution

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

Solution steps

\frac{d}{d x} (x e^{- 4 x})

Apply the Product Rule:

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

f = x, g = e^{- 4 x}

= \frac{d x}{d x} e^{- 4 x} + \frac{d}{d x} (e^{- 4 x}) x

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

\frac{d}{d x} (e^{- 4 x}) = - 4 e^{- 4 x}

= 1 \cdot e^{- 4 x} + (- 4 e^{- 4 x}) x

Simplify

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

Popular Examples

(\partial)/(\partial x)(arctan(y^3x))

\frac{\partial}{\partial x} (arctan (y^{3} x))

integral of x/(sqrt(9+x^2))

\int \frac{x}{9 + x ^{2}} d x

derivative of (x^2+3/(sqrt(x^2+1)))

\frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} + 1})

(\partial)/(\partial y)((x^2)/(4-y^2))

\frac{\partial}{\partial y} (\frac{x ^{2}}{4 - y ^{2}})

(\partial)/(\partial p)((p+q)/(p+r))

\frac{\partial}{\partial p} (\frac{p + q}{p + r})

Frequently Asked Questions (FAQ)

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