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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{d}{d x} (\frac{7 x ^{2} - 6 x + 4}{3 x + 2})

\int (6 x + 2 y) d y

x \to 1 lim (x^{\frac{1}{( 1 - x )}})

\frac{d}{d x} (\frac{6}{( x ^{2} + x + 1 ) ^{2}})

f (x) = 5 - x

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