What is the derivative of 1/4 e^x+3/4 e^{-x} ?

The derivative of 1/4 e^x+3/4 e^{-x} is 1/4 e^x-3/4 e^{-x}

What is the first derivative of 1/4 e^x+3/4 e^{-x} ?

The first derivative of 1/4 e^x+3/4 e^{-x} is 1/4 e^x-3/4 e^{-x}

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\frac{d}{d x} (\frac{1}{4} e^{x} + \frac{3}{4} e^{- x})

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

Solution steps

\frac{d}{d x} (\frac{1}{4} e^{x} + \frac{3}{4} e^{- x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{1}{4} e^{x}) + \frac{d}{d x} (\frac{3}{4} e^{- x})

\frac{d}{d x} (\frac{1}{4} e^{x}) = \frac{1}{4} e^{x}

\frac{d}{d x} (\frac{3}{4} e^{- x}) = - \frac{3}{4} e^{- x}

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

What is the derivative of 1/4 e^x+3/4 e^{-x} ?
The derivative of 1/4 e^x+3/4 e^{-x} is 1/4 e^x-3/4 e^{-x}
What is the first derivative of 1/4 e^x+3/4 e^{-x} ?
The first derivative of 1/4 e^x+3/4 e^{-x} is 1/4 e^x-3/4 e^{-x}