What is (\partial)/(\partial y)(1+ye^{xy}) ?

The answer to (\partial)/(\partial y)(1+ye^{xy}) is e^{yx}+e^{yx}yx

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(\partial)/(\partial y)(1+ye^{xy})

\frac{\partial}{\partial y} (1 + y e^{x y})

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

Solution steps

\frac{\partial}{\partial y} (1 + y e^{x y})

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (1) + \frac{\partial}{\partial y} (y e^{x y})

\frac{\partial}{\partial y} (1) = 0

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

= 0 + e^{x y} + x e^{x y} y

Simplify

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

\int_{1}^{4} (x ln (x)) d x

\frac{d}{d x} (y e^{- x})

\frac{d P}{d t} = a P - b P^{2}

x \to 2 lim (\frac{( x + 3 )}{x - 2})

\frac{d y}{d x} = \frac{e ^{x}}{6 + e ^{x}}

What is (\partial)/(\partial y)(1+ye^{xy}) ?
The answer to (\partial)/(\partial y)(1+ye^{xy}) is e^{yx}+e^{yx}yx