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Popular >

derivative of cxe^{-x}

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

= c \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}

= c (\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}

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

Simplify

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

Popular Examples

integral of 2x*sin(x)e^x

\int 2 x \cdot sin (x) e^{x} d x

t*ty^{''}+5ty^'+4y=0

t \cdot t y^{^{''}} + 5 t y^{^{'}} + 4 y = 0

((sqrt(x^2+25))/2+(9-x)/3)^'

(\frac{x ^{2} + 25}{2} + \frac{9 - x}{3})^{^{'}}

integral of x^7-4x^{-3}+1

\int x^{7} - 4 x^{- 3} + 1 d x

integral of 4xe^{-x^2}

\int 4 x e^{- x^{2}} d x

Frequently Asked Questions (FAQ)

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