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

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

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

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

3 e^{3 x y} x^{3}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (3 x y) = 3 x

= x^{2} e^{3 x y} \cdot 3 x

Simplify

x^{2} e^{3 x y} \cdot 3 x : 3 e^{3 x y} x^{3}

= 3 e^{3 x y} x^{3}

- \frac{x ^{4}}{y ^{4}}

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