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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

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

\frac{d}{d x} (\frac{20 x}{x ^{2} - 5})

(x^{\frac{3}{2}})^{^{'}}

\frac{d}{d x} (\frac{3 x ^{2} - 3}{2 x})

\int 2 x^{2} e^{x} d x

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