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

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

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

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

- 2 e^{- y} y x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (y) = 0

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

= 0 - 2 y e^{- y} x

Simplify

= - 2 e^{- y} y x

sin (x^{2}), 0

y^{^{''}} + y^{^{'}} - 2 y = sin (x)

\frac{d y}{d x} - y = e^{2 x} y^{3}

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

\int \frac{1}{( t + 4 ) ( t - 1 )} d t

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