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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

x \to 0 lim (sin (1))

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

s l o p e (- 1, 6), (2, - 3)

a re a x + y^{2} = 56, x = y

\int \frac{x ^{2} - 1}{2 x - 1} d x

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