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

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

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

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

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

Solution steps

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

Treat

x

as a constant

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

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

\int_{1}^{2} t^{4} f (t^{5}) d t

y = 5 x^{3} - 5 x, (- 1, 0)

\frac{1000}{s + 1000}

\frac{d}{d x} (\frac{2 2}{x ^{2}})

\int arctan (8 x) d x

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