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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

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

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

\int \frac{1}{sin ^{2} ( \frac{x}{2} ) cos ^{2} ( \frac{x}{2} )} d x

\frac{d}{d x} (ln (\frac{4 x}{x ^{2} + 5}))

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

x \to 2 lim ((x^{2} - 4)^{- 1} sin (x - 2))

y^{^{''}} + 4 y = 6 sin (3 t)

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