What is (\partial)/(\partial y)(2x-y/x) ?

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

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(\partial)/(\partial y)(2x-y/x)

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

- \frac{1}{x}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (2 x) = 0

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

= 0 - \frac{1}{x}

Simplify

= - \frac{1}{x}

\frac{d}{d x} (\frac{x ^{2} - 4}{x + 0.5})

y \to 0 lim (a x^{2} + b x^{3})

f (x) = 2 e^{x} (cos (x) - sin (x))

30 y^{^{''}} + 19 y^{^{'}} - 5 y = 0

(3, 4), (5, - 4)

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