What is (\partial)/(\partial x)((x-2)(1-e^{-x})) ?

The answer to (\partial)/(\partial x)((x-2)(1-e^{-x})) is e^{-x}x-3e^{-x}+1

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(\partial)/(\partial x)((x-2)(1-e^{-x}))

\frac{\partial}{\partial x} ((x - 2) (1 - e^{- x}))

e^{- x} x - 3 e^{- x} + 1

Solution steps

\frac{\partial}{\partial x} ((x - 2) (1 - e^{- x}))

Apply the Product Rule:

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

f = x - 2, g = 1 - e^{- x}

= \frac{\partial}{\partial x} (x - 2) (1 - e^{- x}) + \frac{\partial}{\partial x} (1 - e^{- x}) (x - 2)

\frac{\partial}{\partial x} (x - 2) = 1

\frac{\partial}{\partial x} (1 - e^{- x}) = e^{- x}

= 1 \cdot (1 - e^{- x}) + e^{- x} (x - 2)

Simplify

1 \cdot (1 - e^{- x}) + e^{- x} (x - 2) : e^{- x} x - 3 e^{- x} + 1

= e^{- x} x - 3 e^{- x} + 1

\frac{1}{4} y^{^{''}} + 4 t = 2 tan (4 t) - \frac{1}{3} e^{t}

x \to 0 lim (\frac{sec ( x ) - 1}{x})

\frac{d}{d x} (\frac{1}{4 x - 1})

\int \frac{sec ( 2 y ) tan ( 2 y )}{4 + sec ( 2 y )} d y

- 2 x^{4} + 7 x e^{3 x - 2}

What is (\partial)/(\partial x)((x-2)(1-e^{-x})) ?
The answer to (\partial)/(\partial x)((x-2)(1-e^{-x})) is e^{-x}x-3e^{-x}+1