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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

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

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

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

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

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

\frac{d}{d x} (x^{3} (x^{2} + 4 + \frac{1}{x}))

\frac{d}{d x} (x^{2} + 2 y^{2} + z^{2} - 6 x + 3 y - 2 z + 5)

y^{^{''}} - 6 y^{^{'}} + 0 y = 0

\int \frac{5}{e ^{x} + 2} d x

\int_{0}^{1} \frac{1}{2 - 3 x} d x

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