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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

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

= 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

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

\int_{1}^{2} (x + 1) d x

\int x (4 x^{2} + 3)^{3} d x

\frac{d}{d x} (x ln (3 x))

y = (x^{3} + 1) (x^{2} - 2)

y^{^{''}} + 15 y^{^{'}} - 56 y = 0

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