What is (\partial)/(\partial y)(2/(2x+3y)) ?

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

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(\partial)/(\partial y)(2/(2x+3y))

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

= 2 \frac{\partial}{\partial y} (\frac{1}{2 x + 3 y})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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