What is the derivative of (sqrt(x)/(x+y)) ?

The derivative of (sqrt(x)/(x+y)) is (-x-2x\frac{dy)/(dx)+y}{2sqrt(x)(x+y)^2}

What is the first derivative of (sqrt(x)/(x+y)) ?

The first derivative of (sqrt(x)/(x+y)) is (-x-2x\frac{dy)/(dx)+y}{2sqrt(x)(x+y)^2}

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\frac{d}{d x} (\frac{x}{x + y})

\frac{- x - 2 x \frac{d y}{d x} + y}{2 x ( x + y ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x + y})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ) ( x + y ) - \frac{d}{d x} ( x + y ) x}{( x + y ) ^{2}}

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

\frac{d}{d x} (x + y) = 1 + \frac{d y}{d x}

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

Simplify

\frac{\frac{1}{2 x} ( x + y ) - ( 1 + \frac{d y}{d x} ) x}{( x + y ) ^{2}} : \frac{- x - 2 x \frac{d y}{d x} + y}{2 x ( x + y ) ^{2}}

= \frac{- x - 2 x \frac{d y}{d x} + y}{2 x ( x + y ) ^{2}}

What is the derivative of (sqrt(x)/(x+y)) ?
The derivative of (sqrt(x)/(x+y)) is (-x-2x\frac{dy)/(dx)+y}{2sqrt(x)(x+y)^2}
What is the first derivative of (sqrt(x)/(x+y)) ?
The first derivative of (sqrt(x)/(x+y)) is (-x-2x\frac{dy)/(dx)+y}{2sqrt(x)(x+y)^2}