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

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

ln (4 + x^{2})

\int_{1}^{2} 15 4 x^{2} - 3 d x

x \to \infty lim (\frac{1}{8})

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)