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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

3 cos (x) - 2 sin (x)

\int 3 x^{2} + 2 d x

x \to 0 + lim (x - 1)

y = 5 x, x = 5

n = 1 \sum \infty e^{- 4 n}

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