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Popular Calculus >

derivative of 5xe^{-x}

Solution

\frac{d}{d x} (5 x e^{- x})

Solution

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

Solution steps

\frac{d}{d x} (5 x e^{- x})

Take the constant out:

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

= 5 \frac{d}{d x} (x e^{- x})

Apply the Product Rule:

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

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

= 5 (\frac{d x}{d x} e^{- x} + \frac{d}{d x} (e^{- x}) x)

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

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

= 5 (1 \cdot e^{- x} + (- e^{- x}) x)

Simplify

= 5 (e^{- x} - e^{- x} x)

Graph

Popular Examples

integral from-4 to-1 of-4/(x^3)

\int_{- 4}^{- 1} - \frac{4}{x ^{3}} d x

y^{^{'}} + 3 y = e^{t}

tangent of f(x)=110x-16x^2,\at

t an g e n t f (x) = 110 x - 16 x^{2}, at

parity y=ln|sqrt(e^{1+x^2)+3x^4}+cot^2(pix)|

p a r i t y y = ln e^{1 + x^{2}} + 3 x^{4} + cot^{2} (π x)

limit as x approaches 0-of 1/x-1/x

x \to 0 - lim (\frac{1}{x} - \frac{1}{x})

Frequently Asked Questions (FAQ)

What is the derivative of 5xe^{-x} ?
The derivative of 5xe^{-x} is 5(e^{-x}-e^{-x}x)
What is the first derivative of 5xe^{-x} ?
The first derivative of 5xe^{-x} is 5(e^{-x}-e^{-x}x)