What is (\partial)/(\partial x)((6y)/((x+y)^2)) ?

The answer to (\partial)/(\partial x)((6y)/((x+y)^2)) is -(12y)/((x+y)^3)

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(\partial)/(\partial x)((6y)/((x+y)^2))

\frac{\partial}{\partial x} (\frac{6 y}{( x + y ) ^{2}})

- \frac{12 y}{( x + y ) ^{3}}

Solution steps

\frac{\partial}{\partial x} (\frac{6 y}{( x + y ) ^{2}})

Treat

y

as a constant

Take the constant out:

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

= 6 y \frac{\partial}{\partial x} (\frac{1}{( x + y ) ^{2}})

Apply exponent rule:

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

= 6 y \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

= 6 y (- \frac{2}{( x + y ) ^{3}} \cdot 1)

Simplify

6 y (- \frac{2}{( x + y ) ^{3}} \cdot 1) : - \frac{12 y}{( x + y ) ^{3}}

= - \frac{12 y}{( x + y ) ^{3}}

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What is (\partial)/(\partial x)((6y)/((x+y)^2)) ?
The answer to (\partial)/(\partial x)((6y)/((x+y)^2)) is -(12y)/((x+y)^3)