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Popular >

derivative of (7e^x+5e^{-x})/8

Solution

derivative of

\frac{7 e ^{x} + 5 e ^{- x}}{8}

Solution

\frac{1}{8} (7 e^{x} - 5 e^{- x})

Solution steps

\frac{d}{d x} (\frac{7 e ^{x} + 5 e ^{- x}}{8})

Take the constant out:

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

= \frac{1}{8} \frac{d}{d x} (7 e^{x} + 5 e^{- x})

Apply the Sum/Difference Rule:

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

= \frac{1}{8} (\frac{d}{d x} (7 e^{x}) + \frac{d}{d x} (5 e^{- x}))

\frac{d}{d x} (7 e^{x}) = 7 e^{x}

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

= \frac{1}{8} (7 e^{x} - 5 e^{- x})

Popular Examples

area 6x^2,x^2+12 area

6 x^{2}, x^{2} + 12

derivative of (x^9e^x/(x^9+e^x))

\frac{d}{d x} (\frac{x ^{9} e ^{x}}{x ^{9} + e ^{x}})

sum from n=1 to infinity of 2ne^{-n^2}

n = 1 \sum \infty 2 n e^{- n^{2}}

(y^3-2x^2y)dx+2x^3dy=0

(y^{3} - 2 x^{2} y) d x + 2 x^{3} d y = 0

integral of x^3sqrt(x^2+7)

\int x^{3} x^{2} + 7 d x

Frequently Asked Questions (FAQ)

What is the derivative of (7e^x+5e^{-x})/8 ?
The derivative of (7e^x+5e^{-x})/8 is 1/8 (7e^x-5e^{-x})
What is the first derivative of (7e^x+5e^{-x})/8 ?
The first derivative of (7e^x+5e^{-x})/8 is 1/8 (7e^x-5e^{-x})