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

The answer to (\partial)/(\partial y)(xe^{xy+1}) is e^{xy+1}x^2

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

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

e^{x y + 1} x^{2}

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

= x e^{x y + 1} x

Simplify

x e^{x y + 1} x : e^{x y + 1} x^{2}

= e^{x y + 1} x^{2}

What is (\partial)/(\partial y)(xe^{xy+1}) ?
The answer to (\partial)/(\partial y)(xe^{xy+1}) is e^{xy+1}x^2