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

The derivative of y((x-y)/(x+y)) is (x-y)/(x+y)-(2xy)/((x+y)^2)

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

The first derivative of y((x-y)/(x+y)) is (x-y)/(x+y)-(2xy)/((x+y)^2)

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derivative of

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

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

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = \frac{x - y}{x + y}

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

\frac{d y}{d y} = 1

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

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

Simplify

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

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

\int \frac{1}{16 x ^{2} + 2} d x

\frac{d}{d x} (5 x + 9)

\frac{d}{d x} (cosh (x))

\int \frac{1}{y ^{2} y ^{2} + 25} d y

\frac{d}{d x} (7 cos^{2} (x))

What is the derivative of y((x-y)/(x+y)) ?
The derivative of y((x-y)/(x+y)) is (x-y)/(x+y)-(2xy)/((x+y)^2)
What is the first derivative of y((x-y)/(x+y)) ?
The first derivative of y((x-y)/(x+y)) is (x-y)/(x+y)-(2xy)/((x+y)^2)