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

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

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

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

y = e^{5 x}

x^{3} - 8 x^{2}

\int_{- 1}^{1} (1 - x^{2}) d x

f (x) = x^{2} x - 5 x

\frac{d}{d x} (3 e^{\frac{x}{4}})

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