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Popular >

derivative of y= 1/2 (e^x+e^{-x})

Solution

derivative of

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

Solution

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

Solution steps

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

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

integral of 2x(x^2-7)^{99}

\int 2 x (x^{2} - 7)^{99} d x

(\partial)/(\partial y)(e^{xyz^8}yz^8)

\frac{\partial}{\partial y} (e^{x y z^{8}} y z^{8})

limit as x approaches 0 of (sin(x))^{5x}

x \to 0 lim ((sin (x))^{5 x})

limit as x approaches 4 of 2/(sqrt(x-4))

x \to 4 lim (\frac{2}{x - 4})

integral of sec^2(4x)(3-tan(4x))^3

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

Frequently Asked Questions (FAQ)

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