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

The answer to (\partial)/(\partial x)(x/(y^2)+xy+2) is y+1/(y^2)

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

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

y + \frac{1}{y ^{2}}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial x} (2) = 0

= \frac{1}{y ^{2}} + y + 0

Simplify

= y + \frac{1}{y ^{2}}

x^{2} + 5

\frac{d}{d x} (\frac{x ^{3}}{3} + 7 x^{2} + 50 x)

\frac{\partial}{\partial x} (5 arccot (x))

\frac{d}{d x} ((2 x - 8)^{4} (x^{2} + x + 1)^{5})

\int \frac{e ^{x - y}}{1 + e ^{x}}

What is (\partial)/(\partial x)(x/(y^2)+xy+2) ?
The answer to (\partial)/(\partial x)(x/(y^2)+xy+2) is y+1/(y^2)