What is (\partial)/(\partial y)(1+ln(x)+y/x) ?

The answer to (\partial)/(\partial y)(1+ln(x)+y/x) is 1/x

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(\partial)/(\partial y)(1+ln(x)+y/x)

\frac{\partial}{\partial y} (1 + ln (x) + \frac{y}{x})

\frac{1}{x}

Solution steps

\frac{\partial}{\partial y} (1 + ln (x) + \frac{y}{x})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (1) = 0

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

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

= 0 + 0 + \frac{1}{x}

Simplify

= \frac{1}{x}

\int e^{4 x^{2}} d x

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

\frac{\partial}{\partial y} (\frac{18 x y}{x + y})

arccsc (x^{4} + 1)

n \to \infty lim (2^{\frac{1}{n}})

What is (\partial)/(\partial y)(1+ln(x)+y/x) ?
The answer to (\partial)/(\partial y)(1+ln(x)+y/x) is 1/x