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

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

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

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

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

Solution steps

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

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

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

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

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

\int - 3 x + 2 d x

25 \cdot 1. 6^{t}

\frac{\partial}{\partial x} (\frac{y}{2 1 + x y})

\int_{1}^{4} 24 t d t

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

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