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

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

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(\partial)/(\partial x)(((x-y))/(xy+3))

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

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

Solution steps

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

Treat

y

as a constant

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int cos^{4} (8 x) d x

x \to 0 lim (\frac{3 x ^{2} + 5 x}{x})

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

\int x^{3} x - 2 d x

\frac{d}{d x} (x^{3} - 5 x^{2} + 4 x - 20 - 5 e^{3 x})

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