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

The answer to (\partial)/(\partial y)(xe^{xy^2}) is 2e^{xy^2}x^2y

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(\partial)/(\partial y)(xe^{xy^2})

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

2 e^{x y^{2}} x^{2} y

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= x e^{x y^{2}} \cdot 2 x y

Simplify

x e^{x y^{2}} \cdot 2 x y : 2 e^{x y^{2}} x^{2} y

= 2 e^{x y^{2}} x^{2} y

x \to - 1 - lim (- 4 x - 4 - 8)

y^{^{'}} + y = \frac{1 - x}{2 x ^{2}}

y^{6} + x^{3} = y^{2} + 12 x, (0, 1)

x \to - 1 lim (\frac{x}{0})

What is (\partial)/(\partial y)(xe^{xy^2}) ?
The answer to (\partial)/(\partial y)(xe^{xy^2}) is 2e^{xy^2}x^2y