What is the d/(dy)((x)(1-xe^{-x})) ?

The d/(dy)((x)(1-xe^{-x})) is e^{-y}y^2-2e^{-y}y+1

What is the first d/(dy)((x)(1-xe^{-x})) ?

The first d/(dy)((x)(1-xe^{-x})) is e^{-y}y^2-2e^{-y}y+1

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\frac{d}{d y} ((y) (1 - y e^{- y}))

e^{- y} y^{2} - 2 e^{- y} y + 1

Solution steps

\frac{d}{d y} ((y) (1 - y e^{- y}))

Apply the Product Rule:

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

f = y, g = 1 - y e^{- y}

= \frac{d y}{d y} (1 - y e^{- y}) + \frac{d}{d y} (1 - y e^{- y}) y

\frac{d y}{d y} = 1

\frac{d}{d y} (1 - y e^{- y}) = e^{- y} y - e^{- y}

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

Simplify

1 \cdot (1 - y e^{- y}) + (e^{- y} y - e^{- y}) y : e^{- y} y^{2} - 2 e^{- y} y + 1

= e^{- y} y^{2} - 2 e^{- y} y + 1

(x, y) \Rightarrow (x - 5, y - 3)

arcsin (- 8 (x + c))

\frac{8 ( 3 x - 7 )}{5}

13 \cdot (30 - \frac{60}{π})

((2 + x)^{2})^{2}

What is the d/(dy)((x)(1-xe^{-x})) ?
The d/(dy)((x)(1-xe^{-x})) is e^{-y}y^2-2e^{-y}y+1
What is the first d/(dy)((x)(1-xe^{-x})) ?
The first d/(dy)((x)(1-xe^{-x})) is e^{-y}y^2-2e^{-y}y+1