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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

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

f = y^{2}, g = e^{x y - 3}

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

\frac{\partial}{\partial y} (y^{2}) = 2 y

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

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

x \to - 5 lim (\frac{3}{x + 5})

\int \frac{1}{- 2 y} d y

y = 3 sin (\frac{x π}{90})

\int 3 x e^{5 x^{2}} d x

\frac{d y}{d x} = \frac{2 x + sec ^{2} ( x )}{4 y}, y (π) = 1

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