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

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

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

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

y^{^{'}} - 2 y = 3 e^{2 x}

sec^{4} (x)

\int \frac{3}{x ^{2} ( x + 1 )} d x

\int \frac{3 x}{( x ^{2} + 1 )} d x

\frac{d}{d x} (\frac{4 x ^{2} - 16}{x - 2})

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