What is (\partial)/(\partial y)(e^{xy}ln(z)) ?

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

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(\partial)/(\partial y)(e^{xy}ln(z))

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

ln (z) e^{x y} x

Solution steps

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

Treat

x, z

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

= ln (z) e^{x y} x

\int \frac{( ln ( 2 x ) )}{x} d x

x \to 4 lim (f (x))

f (x) = - \frac{1}{x}

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

\int \frac{x ^{4}}{x ^{2} - 9} d x

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