What is the derivative of ae^{-x}+bxe^{-x} ?

The derivative of ae^{-x}+bxe^{-x} is -ae^{-x}+b(e^{-x}-e^{-x}x)

What is the first derivative of ae^{-x}+bxe^{-x} ?

The first derivative of ae^{-x}+bxe^{-x} is -ae^{-x}+b(e^{-x}-e^{-x}x)

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\frac{d}{d x} (a e^{- x} + b x e^{- x})

- a e^{- x} + b (e^{- x} - e^{- x} x)

Solution steps

\frac{d}{d x} (a e^{- x} + b x e^{- x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= - a e^{- x} + b (e^{- x} - e^{- x} x)

x^{2} + 2 x y + 4 y^{2} = 12, (2, 1)

\int (- x^{2} + 6)^{2} - (x^{2} + 4 x)^{2} d x

2 x^{3}

- 27

\frac{1}{s ( s ^{2} + 16 )}

What is the derivative of ae^{-x}+bxe^{-x} ?
The derivative of ae^{-x}+bxe^{-x} is -ae^{-x}+b(e^{-x}-e^{-x}x)
What is the first derivative of ae^{-x}+bxe^{-x} ?
The first derivative of ae^{-x}+bxe^{-x} is -ae^{-x}+b(e^{-x}-e^{-x}x)