What is (\partial}{\partial x}(y+\frac{x^2)/y) ?

The answer to (\partial}{\partial x}(y+\frac{x^2)/y) is (2x)/y

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(\partial}{\partial x}(y+\frac{x^2)/y)

\frac{\partial}{\partial x} (y + \frac{x ^{2}}{y})

\frac{2 x}{y}

Solution steps

\frac{\partial}{\partial x} (y + \frac{x ^{2}}{y})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 0 + \frac{2 x}{y}

Simplify

= \frac{2 x}{y}

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\frac{d}{d a} (1 + sin (a) + cos (a))

\frac{d}{d x} (\frac{100 ( x + 25 )}{x})

\int \frac{6 x - 12}{x ^{2}} d x

What is (\partial}{\partial x}(y+\frac{x^2)/y) ?
The answer to (\partial}{\partial x}(y+\frac{x^2)/y) is (2x)/y