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Popular >

derivative of f(x)=(e^x+e^{-x})/2

Solution

derivative of

f (x) = \frac{e ^{x} + e ^{- x}}{2}

Solution

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

Solution steps

\frac{d}{d x} (\frac{e ^{x} + e ^{- x}}{2})

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Popular Examples

(dy)/(dx)=(5x+2y)/(5x+2y+2)

\frac{d y}{d x} = \frac{5 x + 2 y}{5 x + 2 y + 2}

(d^2y)/(dx^2)=0

\frac{d ^{2} y}{d x ^{2}} = 0

11x-4ysqrt(x^2+1)y^'=0,y(0)=3

11 x - 4 y x^{2} + 1 y^{^{'}} = 0, y (0) = 3

(dy}{dx}=\frac{y+xcos^2(y/x))/x

\frac{d y}{d x} = \frac{y + x cos ^{2} ( \frac{y}{x} )}{x}

derivative of (0.9e^x/(tan(x)))

\frac{d}{d x} (\frac{0.9 e ^{x}}{tan ( x )})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(e^x+e^{-x})/2 ?
The derivative of f(x)=(e^x+e^{-x})/2 is 1/2 (e^x-e^{-x})
What is the first derivative of f(x)=(e^x+e^{-x})/2 ?
The first derivative of f(x)=(e^x+e^{-x})/2 is 1/2 (e^x-e^{-x})