What is the derivative of (e^x/(2x)) ?

The derivative of (e^x/(2x)) is (e^xx-e^x)/(2x^2)

What is the first derivative of (e^x/(2x)) ?

The first derivative of (e^x/(2x)) is (e^xx-e^x)/(2x^2)

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

\frac{e ^{x} x - e ^{x}}{2 x ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

= \frac{1}{2} \cdot \frac{e ^{x} x - 1 \cdot e ^{x}}{x ^{2}}

Simplify

\frac{1}{2} \cdot \frac{e ^{x} x - 1 \cdot e ^{x}}{x ^{2}} : \frac{e ^{x} x - e ^{x}}{2 x ^{2}}

= \frac{e ^{x} x - e ^{x}}{2 x ^{2}}

\frac{d y}{d x} = 500 e^{\frac{1}{10} l n (\frac{625}{500}) 50}

\int e^{6 x} 2^{9 x} d x

\frac{d}{d t} ((cos (t))^{2})

\frac{\partial}{\partial y} (x y e^{- 4 y})

\int \frac{1}{x 7 - x ^{2}} d x

What is the derivative of (e^x/(2x)) ?
The derivative of (e^x/(2x)) is (e^xx-e^x)/(2x^2)
What is the first derivative of (e^x/(2x)) ?
The first derivative of (e^x/(2x)) is (e^xx-e^x)/(2x^2)