What is (\partial)/(\partial x)(y^2(x+y)^{-2}) ?

The answer to (\partial)/(\partial x)(y^2(x+y)^{-2}) is -(2y^2)/((x+y)^3)

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

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

- \frac{2 y ^{2}}{( x + y ) ^{3}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

- \frac{2}{( x + y ) ^{3}} \frac{\partial}{\partial x} (x + y)

= - \frac{2}{( x + y ) ^{3}} \frac{\partial}{\partial x} (x + y)

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

= y^{2} (- \frac{2}{( x + y ) ^{3}} \cdot 1)

Simplify

y^{2} (- \frac{2}{( x + y ) ^{3}} \cdot 1) : - \frac{2 y ^{2}}{( x + y ) ^{3}}

= - \frac{2 y ^{2}}{( x + y ) ^{3}}

\int (tan (\frac{x}{14}))^{5} d x

11 x y^{^{'}} + y = 132 x

(u^{- 2} + u^{- 3}) (u^{5} - 6 u^{2})

\int e^{- x} + 2 d x

\frac{d}{d x} (\frac{9 x}{( x ^{2} + 81 ) ^{\frac{3}{2}}})

What is (\partial)/(\partial x)(y^2(x+y)^{-2}) ?
The answer to (\partial)/(\partial x)(y^2(x+y)^{-2}) is -(2y^2)/((x+y)^3)