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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\int (3 + x^{8})^{4} 8 x^{7} d x

f (x) = x^{2} - \frac{1}{x}, at x = - 1

\frac{d}{d x} (e^{a r c s i n (x)})

\frac{d}{d x} (x + 6 x + 3)

tan (x) + cos^{2} (x) + sin^{2} (x) - 3

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