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

The derivative of (e^{2x}/(sqrt(x))) is (4e^{2x}x-e^{2x})/(2xsqrt(x))

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

The first derivative of (e^{2x}/(sqrt(x))) is (4e^{2x}x-e^{2x})/(2xsqrt(x))

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

\frac{4 e ^{2 x} x - e ^{2 x}}{2 x x}

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

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

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

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

Simplify

\frac{e ^{2 x} \cdot 2 x - \frac{1}{2 x} e ^{2 x}}{( x ) ^{2}} : \frac{4 e ^{2 x} x - e ^{2 x}}{2 x x}

= \frac{4 e ^{2 x} x - e ^{2 x}}{2 x x}

What is the derivative of (e^{2x}/(sqrt(x))) ?
The derivative of (e^{2x}/(sqrt(x))) is (4e^{2x}x-e^{2x})/(2xsqrt(x))
What is the first derivative of (e^{2x}/(sqrt(x))) ?
The first derivative of (e^{2x}/(sqrt(x))) is (4e^{2x}x-e^{2x})/(2xsqrt(x))