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

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

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

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

sin (z) e^{x y} x

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

= sin (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

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

x \to 1 lim (x)

\frac{d}{d x} (4 (x + 4)^{\frac{3}{2}})

\int (\frac{1}{x} + e^{x}) d x

y^{^{''}} + 64 y = 7 tan (8 x)

x \to 0 lim (\frac{x ^{5} + 9 x}{x})

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