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Popular >

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

Solution

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

Solution

\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}

Graph

Popular Examples

derivative of 5ln(x-(x^2)/(40))

\frac{d}{d x} (5 ln (x) - \frac{x ^{2}}{40})

derivative of (1+x^2/x)

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

limit as x approaches 4 of 6/x

x \to 4 lim (\frac{6}{x})

integral of xy^2

\int x y^{2} d x

\frac{6 d u}{d t} = u^{2}

Frequently Asked Questions (FAQ)

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}