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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

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

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

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

\frac{\partial}{\partial x} (x) = 1

= e^{x y} y x + 1 \cdot e^{x y}

Simplify

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

\frac{d}{d x} (sin (x + \frac{π}{2}))

\int (x^{6} - 3 x^{2})^{4} (x^{5} - x) d x

\frac{d}{d t} (3 - 3 t)

\frac{\partial}{\partial x} (cos (x) y)

5 x, x^{2} - 6

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