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Popular >

derivative of (e^x/(sqrt(x)))

Solution

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

Solution

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

Solution steps

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

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

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

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

Simplify

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

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

Graph

Popular Examples

integral of (8x+e^x)sqrt(4x^2+e^x)

\int (8 x + e^{x}) 4 x^{2} + e^{x} d x

(d^2)/(dx^2)(3x^2cos(8x))

\frac{d ^{2}}{d x ^{2}} (3 x^{2} cos (8 x))

limit as x approaches 1 of (ln(x))^{x-1}

x \to 1 lim ((ln (x))^{x - 1})

(dy)/(dx)=9x^2-12x

\frac{d y}{d x} = 9 x^{2} - 12 x

inverse oflaplace 1/((s-1)(s-2)(s-3))inverse laplace

\frac{1}{( s - 1 ) ( s - 2 ) ( s - 3 )}

Frequently Asked Questions (FAQ)

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