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

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

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

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

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derivative of

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

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

Solution steps

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

Simplify

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

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

\int \frac{e ^{2 t}}{1 - e ^{2 t}} d t

\frac{d y}{d x} = x^{8} y^{- 5}

(3 x y^{2} - 3) d x + (3 x^{2} y + 4) d y = 0

\int \frac{( x + 7 ) ^{3}}{2 x} d x

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