What is the derivative of xy+ln(x/y) ?

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

What is the first derivative of xy+ln(x/y) ?

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (ln (\frac{x}{y})) = \frac{y - x \frac{d y}{d x}}{x y}

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

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