What is the derivative of e^{3x}+e^{-2x} ?

The derivative of e^{3x}+e^{-2x} is e^{3x}*3-2e^{-2x}

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

The first derivative of e^{3x}+e^{-2x} is e^{3x}*3-2e^{-2x}

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

e^{3 x} \cdot 3 - 2 e^{- 2 x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= e^{3 x} \cdot 3 - 2 e^{- 2 x}

y^{^{''}} + 6 y^{^{'}} + 15 y = 0

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