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

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

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

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

\frac{x}{y} - \frac{6 y ^{2}}{x ^{3}}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

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

k = 0 \sum \infty \frac{x ^{k}}{k !}

- cos (x), cos^{2} (x), [\frac{- π}{2}, \frac{π}{2}]

\int 12 x d x

\int \frac{3}{t} d t

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