What is (\partial)/(\partial x)(ln(8ye^{xy})) ?

The answer to (\partial)/(\partial x)(ln(8ye^{xy})) is y

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(\partial)/(\partial x)(ln(8ye^{xy}))

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

y

Solution steps

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

Simplify

ln (8 y e^{x y}) : ln (8 y) + y x

= \frac{\partial}{\partial x} (ln (8 y) + y x)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (ln (8 y)) + \frac{\partial}{\partial x} (y x)

\frac{\partial}{\partial x} (ln (8 y)) = 0

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

= 0 + y

Simplify

= y

\int \frac{1}{( 25 - x ^{2} ) ^{2}} d x

3 x^{2} - x^{3}

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

\int_{x}^{3} sin (t^{2}) d t

\frac{d}{d x} (\frac{50}{x ^{7}})

What is (\partial)/(\partial x)(ln(8ye^{xy})) ?
The answer to (\partial)/(\partial x)(ln(8ye^{xy})) is y