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

The answer to (\partial)/(\partial y)(ye^{xy}+y) is e^{xy}+xe^{xy}y+1

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

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

e^{x y} + x e^{x y} y + 1

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (y) = 1

= e^{x y} + x e^{x y} y + 1

x^{3} - 5 x^{2} + 13

3 cos (t)

\frac{d}{d x} (e^{s i n (x)})

\int e^{2 x} + x^{3} d x

x \to 1 lim (10 x)

What is (\partial)/(\partial y)(ye^{xy}+y) ?
The answer to (\partial)/(\partial y)(ye^{xy}+y) is e^{xy}+xe^{xy}y+1