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

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

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(\partial)/(\partial y)(xy^2e^{x^2})

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= x e^{x^{2}} \cdot 2 y^{2 - 1}

Simplify

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

x \to - 1 - lim (2 x^{2} - 4 x + 8)

\frac{\partial}{\partial x} (6 x y + 5 yz + x z - 48)

16 y^{^{''}} + 152 y^{^{'}} + 361 y = 0, y (0) = 9, y^{^{'}} (0) = 2

\frac{\partial}{\partial y} (ln (1 + x^{2} + y))

\int \frac{18}{( x ^{2} - 1 ) ^{2}} d x

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