What is the derivative of a*e^{2x}+b*e^{-3x}+c*e^x ?

The derivative of a*e^{2x}+b*e^{-3x}+c*e^x is ae^{2x}*2-3be^{-3x}+ce^x

What is the first derivative of a*e^{2x}+b*e^{-3x}+c*e^x ?

The first derivative of a*e^{2x}+b*e^{-3x}+c*e^x is ae^{2x}*2-3be^{-3x}+ce^x

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\frac{d}{d x} (a \cdot e^{2 x} + b \cdot e^{- 3 x} + c \cdot e^{x})

a e^{2 x} \cdot 2 - 3 b e^{- 3 x} + c e^{x}

Solution steps

\frac{d}{d x} (a e^{2 x} + b e^{- 3 x} + c e^{x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (a e^{2 x}) + \frac{d}{d x} (b e^{- 3 x}) + \frac{d}{d x} (c e^{x})

\frac{d}{d x} (a e^{2 x}) = a e^{2 x} \cdot 2

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

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

= a e^{2 x} \cdot 2 - 3 b e^{- 3 x} + c e^{x}

What is the derivative of a*e^{2x}+b*e^{-3x}+c*e^x ?
The derivative of a*e^{2x}+b*e^{-3x}+c*e^x is ae^{2x}*2-3be^{-3x}+ce^x
What is the first derivative of a*e^{2x}+b*e^{-3x}+c*e^x ?
The first derivative of a*e^{2x}+b*e^{-3x}+c*e^x is ae^{2x}*2-3be^{-3x}+ce^x