What is (\partial)/(\partial y)((18xy)/(x+y)) ?

The answer to (\partial)/(\partial y)((18xy)/(x+y)) is (18x^2)/((x+y)^2)

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(\partial)/(\partial y)((18xy)/(x+y))

\frac{\partial}{\partial y} (\frac{18 x y}{x + y})

\frac{18 x ^{2}}{( x + y ) ^{2}}

Solution steps

\frac{\partial}{\partial y} (\frac{18 x y}{x + y})

Treat

x

as a constant

Take the constant out:

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

= 18 x \frac{\partial}{\partial y} (\frac{y}{x + y})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 18 x \frac{\frac{\partial}{\partial y} ( y ) ( x + y ) - \frac{\partial}{\partial y} ( x + y ) y}{( x + y ) ^{2}}

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

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

= 18 x \frac{1 \cdot ( x + y ) - 1 \cdot y}{( x + y ) ^{2}}

Simplify

18 x \frac{1 \cdot ( x + y ) - 1 \cdot y}{( x + y ) ^{2}} : \frac{18 x ^{2}}{( x + y ) ^{2}}

= \frac{18 x ^{2}}{( x + y ) ^{2}}

arccsc (x^{4} + 1)

n \to \infty lim (2^{\frac{1}{n}})

y^{^{'}} + e^{x} y = e^{3 x} y^{- 2}

6 - x^{2}, x^{2} - 2

\int \frac{x}{x + 1} d x

What is (\partial)/(\partial y)((18xy)/(x+y)) ?
The answer to (\partial)/(\partial y)((18xy)/(x+y)) is (18x^2)/((x+y)^2)