What is (\partial)/(\partial y)(xye^{-3y}) ?

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

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(\partial)/(\partial y)(xye^{-3y})

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

= x (1 \cdot e^{- 3 y} + (- 3 e^{- 3 y}) y)

Simplify

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

x^{2} - 3 x, 5 x, [0, 8]

x^{2} - 1, 0, 2

\int_{0}^{4} 3 t - 8 d t

\frac{d y}{d x} + y = 2 x y^{2} e x

\frac{1}{4 s + 1}

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