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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

Expand

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

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

f (x) = - \frac{1}{7} (x^{- 7} - x^{14})

x csc (x)

xx y^{^{'}} = y^{2} + 1

5 y^{^{''}} + 25 y^{^{'}} + 1700 y = 0

y = arccos (3 x)

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