What is the derivative of (8e^x+5e^{-x}/8) ?

The derivative of (8e^x+5e^{-x}/8) is e^x-5/8 e^{-x}

What is the first derivative of (8e^x+5e^{-x}/8) ?

The first derivative of (8e^x+5e^{-x}/8) is e^x-5/8 e^{-x}

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Popular >

\frac{d}{d x} (\frac{8 e ^{x} + 5 e ^{- x}}{8})

e^{x} - \frac{5}{8} e^{- x}

Solution steps

\frac{d}{d x} (\frac{8 e ^{x} + 5 e ^{- x}}{8})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{8} \frac{d}{d x} (8 e^{x} + 5 e^{- x})

Apply the Sum/Difference Rule:

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

= \frac{1}{8} (\frac{d}{d x} (8 e^{x}) + \frac{d}{d x} (5 e^{- x}))

\frac{d}{d x} (8 e^{x}) = 8 e^{x}

\frac{d}{d x} (5 e^{- x}) = - 5 e^{- x}

= \frac{1}{8} (8 e^{x} - 5 e^{- x})

Simplify

\frac{1}{8} (8 e^{x} - 5 e^{- x}) : e^{x} - \frac{5}{8} e^{- x}

= e^{x} - \frac{5}{8} e^{- x}

f (x) = 10 - 5 x

\int \frac{4 x ^{5} + 2 x ^{3} + x - 1}{x ^{2}} d x

\int (\frac{1}{x ^{9}} - x^{9} - \frac{1}{2}) d x

\int (x^{3} + 2 x^{2} - 3 x + 4) d x

\int x e^{- \frac{x}{6}} d x

What is the derivative of (8e^x+5e^{-x}/8) ?
The derivative of (8e^x+5e^{-x}/8) is e^x-5/8 e^{-x}
What is the first derivative of (8e^x+5e^{-x}/8) ?
The first derivative of (8e^x+5e^{-x}/8) is e^x-5/8 e^{-x}