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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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