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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (2) = 0

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

= 0 + e^{x y} + x e^{x y} y

Simplify

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

\int \frac{1}{4 + ( x - 2 ) ^{2}} d x

\frac{d y}{d t} = k y^{2}, y (0) = 47

\frac{\partial}{\partial x} ((x^{2} + y^{2})^{\frac{3}{2}})

\frac{\partial}{\partial x} (x^{3} - y^{3} + 2 x y)

x \to 2 lim (3 x - 6)

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