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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

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

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

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

Simplify

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

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

\frac{d h}{d t} = 5 h

1 + x^{2} d y - 1 - y^{2} d x = 0

\int (13 x + 3) d x

x^{a}

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