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Popular >

derivative of 13xe^{-x}

Solution

\frac{d}{d x} (13 x e^{- x})

Solution

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

Solution steps

\frac{d}{d x} (13 x e^{- x})

Take the constant out:

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

= 13 \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}

= 13 (\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}

= 13 (1 \cdot e^{- x} + (- e^{- x}) x)

Simplify

= 13 (e^{- x} - e^{- x} x)

Popular Examples

(\partial)/(\partial v)(1/4 (u-v))

\frac{\partial}{\partial v} (\frac{1}{4} (u - v))

derivative of f(x)=(x-1)^2 derivative of

f (x) = (x - 1)^{2}

sum from n=1 to infinity of e^{1/n}

n = 1 \sum \infty e^{\frac{1}{n}}

limit as x approaches 0 of 1+sqrt(x)

x \to 0 lim (1 + x)

tangent of y=8x^{1/2}+8x^{3/2}+6,\at x=4 tangent of

y = 8 x^{\frac{1}{2}} + 8 x^{\frac{3}{2}} + 6, at x = 4

Frequently Asked Questions (FAQ)

What is the derivative of 13xe^{-x} ?
The derivative of 13xe^{-x} is 13(e^{-x}-e^{-x}x)
What is the first derivative of 13xe^{-x} ?
The first derivative of 13xe^{-x} is 13(e^{-x}-e^{-x}x)