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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

(x + a) e^{3 x} + b

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

\int_{0}^{1} (e^{x}) d x

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

\int_{0}^{1} t e^{- t} d t

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