What is (\partial)/(\partial x)(ln(9ye^{xy})) ?

The answer to (\partial)/(\partial x)(ln(9ye^{xy})) is y

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(\partial)/(\partial x)(ln(9ye^{xy}))

\frac{\partial}{\partial x} (ln (9 y e^{x y}))

y

Solution steps

\frac{\partial}{\partial x} (ln (9 y e^{x y}))

Simplify

ln (9 y e^{x y}) : ln (9 y) + y x

= \frac{\partial}{\partial x} (ln (9 y) + y x)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (ln (9 y)) + \frac{\partial}{\partial x} (y x)

\frac{\partial}{\partial x} (ln (9 y)) = 0

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

= 0 + y

Simplify

= y

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What is (\partial)/(\partial x)(ln(9ye^{xy})) ?
The answer to (\partial)/(\partial x)(ln(9ye^{xy})) is y