What is the derivative of x/y+y/x ?

The derivative of x/y+y/x is (y-x\frac{dy)/(dx)}{y^2}+(x\frac{dy)/(dx)-y}{x^2}

What is the first derivative of x/y+y/x ?

The first derivative of x/y+y/x is (y-x\frac{dy)/(dx)}{y^2}+(x\frac{dy)/(dx)-y}{x^2}

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

What is the derivative of x/y+y/x ?
The derivative of x/y+y/x is (y-x\frac{dy)/(dx)}{y^2}+(x\frac{dy)/(dx)-y}{x^2}
What is the first derivative of x/y+y/x ?
The first derivative of x/y+y/x is (y-x\frac{dy)/(dx)}{y^2}+(x\frac{dy)/(dx)-y}{x^2}