What is (\partial)/(\partial y)(6ye^{2xy}+x) ?

The answer to (\partial)/(\partial y)(6ye^{2xy}+x) is 6(e^{2yx}+2e^{2yx}yx)

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(\partial)/(\partial y)(6ye^{2xy}+x)

\frac{\partial}{\partial y} (6 y e^{2 x y} + x)

6 (e^{2 y x} + 2 e^{2 y x} y x)

Solution steps

\frac{\partial}{\partial y} (6 y e^{2 x y} + x)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (6 y e^{2 x y}) + \frac{\partial}{\partial y} (x)

\frac{\partial}{\partial y} (6 y e^{2 x y}) = 6 (e^{2 x y} + 2 x e^{2 x y} y)

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

= 6 (e^{2 x y} + 2 x e^{2 x y} y) + 0

Simplify

= 6 (e^{2 y x} + 2 e^{2 y x} y x)

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What is (\partial)/(\partial y)(6ye^{2xy}+x) ?
The answer to (\partial)/(\partial y)(6ye^{2xy}+x) is 6(e^{2yx}+2e^{2yx}yx)