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

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

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

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

e^{x y} x

Solution steps

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

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (z) = 0

= e^{x y} x - 0

Simplify

= e^{x y} x

y^{^{''}} + 12 y^{^{'}} + 37 y = 0

x \to - 5 - lim (\frac{- 2}{x ^{2} - 25})

\int \frac{8}{64 - x ^{2}} d x

\frac{18 x + 4 x ^{2}}{( 9 + 4 x ) ^{2}}

\int e^{- x} cos (a x) d x

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