What is the derivative of xe^{-x}+e^{3x} ?

The derivative of xe^{-x}+e^{3x} is e^{-x}-e^{-x}x+e^{3x}*3

What is the first derivative of xe^{-x}+e^{3x} ?

The first derivative of xe^{-x}+e^{3x} is e^{-x}-e^{-x}x+e^{3x}*3

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\frac{d}{d x} (x e^{- x} + e^{3 x})

e^{- x} - e^{- x} x + e^{3 x} \cdot 3

Solution steps

\frac{d}{d x} (x e^{- x} + e^{3 x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x e^{- x}) + \frac{d}{d x} (e^{3 x})

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

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

= e^{- x} - e^{- x} x + e^{3 x} \cdot 3

What is the derivative of xe^{-x}+e^{3x} ?
The derivative of xe^{-x}+e^{3x} is e^{-x}-e^{-x}x+e^{3x}*3
What is the first derivative of xe^{-x}+e^{3x} ?
The first derivative of xe^{-x}+e^{3x} is e^{-x}-e^{-x}x+e^{3x}*3