What is (\partial)/(\partial x)(y^2e^{xy-3}) ?

The answer to (\partial)/(\partial x)(y^2e^{xy-3}) is e^{yx-3}y^3

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(\partial)/(\partial x)(y^2e^{xy-3})

\frac{\partial}{\partial x} (y^{2} e^{x y - 3})

e^{y x - 3} y^{3}

Solution steps

\frac{\partial}{\partial x} (y^{2} e^{x y - 3})

Treat

y

as a constant

Take the constant out:

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

= y^{2} \frac{\partial}{\partial x} (e^{x y - 3})

Apply the chain rule:

e^{x y - 3} \frac{\partial}{\partial x} (x y - 3)

= e^{x y - 3} \frac{\partial}{\partial x} (x y - 3)

\frac{\partial}{\partial x} (x y - 3) = y

= y^{2} e^{x y - 3} y

Simplify

y^{2} e^{x y - 3} y : e^{y x - 3} y^{3}

= e^{y x - 3} y^{3}

What is (\partial)/(\partial x)(y^2e^{xy-3}) ?
The answer to (\partial)/(\partial x)(y^2e^{xy-3}) is e^{yx-3}y^3