What is (\partial)/(\partial x)(2xye^{xy^2}-3y^2) ?

The answer to (\partial)/(\partial x)(2xye^{xy^2}-3y^2) is 2y(e^{xy^2}+e^{xy^2}xy^2)

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(\partial)/(\partial x)(2xye^{xy^2}-3y^2)

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

2 y (e^{x y^{2}} + e^{x y^{2}} x y^{2})

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (3 y^{2}) = 0

= 2 y (e^{y^{2} x} + y^{2} e^{y^{2} x} x) - 0

Simplify

= 2 y (e^{x y^{2}} + e^{x y^{2}} x y^{2})

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

\frac{\partial}{\partial y} (2 arctan (\frac{y}{x}))

f (x) = 2 + 3 x - 5 x^{2}, at x = 1

h \to 1 lim (4 h^{2} + x + 3)

\frac{d}{d x} (e^{x} sin (9 x))

What is (\partial)/(\partial x)(2xye^{xy^2}-3y^2) ?
The answer to (\partial)/(\partial x)(2xye^{xy^2}-3y^2) is 2y(e^{xy^2}+e^{xy^2}xy^2)