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

The answer to (\partial)/(\partial x)(e^{xy}+x/y) is e^{xy}y+1/y

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

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

e^{x y} y + \frac{1}{y}

Solution steps

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

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{x}{y})

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

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

= e^{x y} y + \frac{1}{y}

y^{^{''}} + 13 y^{^{'}} + 42 y = 0

y^{^{''}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = 0

\int \frac{x ^{6}}{6} d x

\int_{2}^{8} x d x

\int cos^{3} (x s i) n^{4} x d x

What is (\partial)/(\partial x)(e^{xy}+x/y) ?
The answer to (\partial)/(\partial x)(e^{xy}+x/y) is e^{xy}y+1/y