What is (\partial)/(\partial x)(2e^{-2x}+1/3 e^x) ?

The answer to (\partial)/(\partial x)(2e^{-2x}+1/3 e^x) is -4e^{-2x}+1/3 e^x

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(\partial)/(\partial x)(2e^{-2x}+1/3 e^x)

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (2 e^{- 2 x}) = - 4 e^{- 2 x}

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

= - 4 e^{- 2 x} + \frac{1}{3} e^{x}

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What is (\partial)/(\partial x)(2e^{-2x}+1/3 e^x) ?
The answer to (\partial)/(\partial x)(2e^{-2x}+1/3 e^x) is -4e^{-2x}+1/3 e^x