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

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

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

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

- \frac{1}{x ^{2}}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 0 - \frac{1}{x ^{2}}

Simplify

= - \frac{1}{x ^{2}}

\int \frac{sin ^{3} ( x )}{cos ( x )} d x

x^{2} y^{^{'}} + \frac{4}{3} x y = 3 cos (3 x) y^{- \frac{1}{2}}

y = 3 x, x = 3, y = 1

y^{^{'}} + y = x y^{2}

x \to \infty lim (2 x^{2} + 5)

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