What is the derivative of e^{-2x}+1/3 e^x ?

The derivative of e^{-2x}+1/3 e^x is -2e^{-2x}+1/3 e^x

What is the first derivative of e^{-2x}+1/3 e^x ?

The first derivative of e^{-2x}+1/3 e^x is -2e^{-2x}+1/3 e^x

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derivative of

e^{- 2 x} + \frac{1}{3} e^{x}

- 2 e^{- 2 x} + \frac{1}{3} e^{x}

Solution steps

\frac{d}{d x} (e^{- 2 x} + \frac{1}{3} e^{x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (e^{- 2 x}) + \frac{d}{d x} (\frac{1}{3} e^{x})

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

\frac{d}{d x} (\frac{1}{3} e^{x}) = \frac{1}{3} e^{x}

= - 2 e^{- 2 x} + \frac{1}{3} e^{x}

What is the derivative of e^{-2x}+1/3 e^x ?
The derivative of e^{-2x}+1/3 e^x is -2e^{-2x}+1/3 e^x
What is the first derivative of e^{-2x}+1/3 e^x ?
The first derivative of e^{-2x}+1/3 e^x is -2e^{-2x}+1/3 e^x