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

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

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

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

y e^{- y} (3 - 2 x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

x \to 0 lim (x^{2} cos (\frac{7}{x}))

(4 e^{x})^{^{'}}

\frac{7 x}{e ^{x}}

\frac{d}{d x} (8^{- 3 x^{2}})

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