What is (\partial)/(\partial x)(y/(x+y)) ?

The answer to (\partial)/(\partial x)(y/(x+y)) is -y/((x+y)^2)

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(\partial)/(\partial x)(y/(x+y))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = 10 - x^{2}

7 x^{2} \frac{d y}{d x} = \frac{d y}{d x} + 7 x e^{- y}

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

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

\frac{1}{x ^{2}}, 3

What is (\partial)/(\partial x)(y/(x+y)) ?
The answer to (\partial)/(\partial x)(y/(x+y)) is -y/((x+y)^2)