What is the derivative of y=e^{-x}-e^{-x}x ?

The derivative of y=e^{-x}-e^{-x}x is e^{-x}x-2e^{-x}

What is the first derivative of y=e^{-x}-e^{-x}x ?

The first derivative of y=e^{-x}-e^{-x}x is e^{-x}x-2e^{-x}

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derivative of

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

e^{- x} x - 2 e^{- x}

Solution steps

\frac{d}{d x} (e^{- x} - e^{- x} x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (e^{- x}) - \frac{d}{d x} (e^{- x} x)

\frac{d}{d x} (e^{- x}) = - e^{- x}

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

= - e^{- x} - (- e^{- x} x + e^{- x})

Simplify

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

\frac{d}{d x} (2 e^{x} + e^{x} x)

\int 2 x x - \frac{1}{x} d x

\frac{d}{d x} (ln (52 x))

\frac{d y}{d x} + 9 x y = 8 x

\int_{0}^{6} \frac{π}{9} (36 - y^{2}) d y

What is the derivative of y=e^{-x}-e^{-x}x ?
The derivative of y=e^{-x}-e^{-x}x is e^{-x}x-2e^{-x}
What is the first derivative of y=e^{-x}-e^{-x}x ?
The first derivative of y=e^{-x}-e^{-x}x is e^{-x}x-2e^{-x}