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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = e^{x^{2} y}

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

\frac{\partial}{\partial y} (y) = 1

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

= 2 x (1 \cdot e^{x^{2} y} + e^{x^{2} y} x^{2} y)

Simplify

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

y y^{^{'}} = 2 x^{3}

y = 78 - 12 cos (x)

x \to 0 lim (\frac{1 - 1}{x ^{2}})

t \to 0 lim ((t + e^{t})^{\frac{2}{t}})

\frac{d x}{3 d t} - 2 e^{- t} = - x

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