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

The answer to (\partial)/(\partial x)(x^2e^{3xy}) is 2xe^{3xy}+e^{3xy}*3yx^2

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

f = x^{2}, g = e^{3 x y}

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

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

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

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

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What is (\partial)/(\partial x)(x^2e^{3xy}) ?
The answer to (\partial)/(\partial x)(x^2e^{3xy}) is 2xe^{3xy}+e^{3xy}*3yx^2