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

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

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

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

- \frac{y}{x ^{2}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= - \frac{y}{x ^{2}}

\int (5 x^{4} - 8 x^{3} + 9 x^{2} - 2 x + 7) d x

y^{^{'}} = y^{5}

\frac{d}{d x} (\frac{3 x - 5}{2 x + 3})

x \to 0 lim ((sin (\frac{x}{2}))^{x})

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

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