What is (\partial)/(\partial x)(ln(3ye^{xy})) ?

The answer to (\partial)/(\partial x)(ln(3ye^{xy})) is y

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(\partial)/(\partial x)(ln(3ye^{xy}))

\frac{\partial}{\partial x} (ln (3 y e^{x y}))

y

Solution steps

\frac{\partial}{\partial x} (ln (3 y e^{x y}))

Simplify

ln (3 y e^{x y}) : ln (3 y) + y x

= \frac{\partial}{\partial x} (ln (3 y) + y x)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (ln (3 y)) + \frac{\partial}{\partial x} (y x)

\frac{\partial}{\partial x} (ln (3 y)) = 0

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

= 0 + y

Simplify

= y

\frac{\partial}{\partial x} (8 y e^{x} - ln (z))

\frac{( s + 1 ) ^{3}}{s ^{6}}

\int \frac{1}{( 3 + y ) ^{5}} d y

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

\frac{x ^{2}}{x - 1}

What is (\partial)/(\partial x)(ln(3ye^{xy})) ?
The answer to (\partial)/(\partial x)(ln(3ye^{xy})) is y