What is (\partial)/(\partial x)(e^{xy}+y/x) ?

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

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(\partial)/(\partial x)(e^{xy}+y/x)

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

e^{x y} y - \frac{y}{x ^{2}}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= e^{x y} y - \frac{y}{x ^{2}}

g (x) = \frac{9}{x ^{3}}

\frac{\partial}{\partial x} (x^{2} - 3 x y^{2})

\int \frac{25}{1 + 25 x ^{2}} d x

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

\int 3 x^{2} - 1 d x

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