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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (y) = 0

= \frac{1}{y ^{2}} (2 x + 0)

Simplify

\frac{1}{y ^{2}} (2 x + 0) : \frac{2 x}{y ^{2}}

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

y^{^{''}} - 4 y^{^{'}} + 8 y = 0

f (x) = arcsin (\frac{x}{4})

\int x^{- \frac{1}{6}} d x

\int_{- 2}^{2} \frac{1}{4 - x ^{2}} d x

y = 6 x + \frac{10}{3}

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