What is the derivative of A(e^{-x}-e^{-x}x) ?

The derivative of A(e^{-x}-e^{-x}x) is A(e^{-x}x-2e^{-x})

What is the first derivative of A(e^{-x}-e^{-x}x) ?

The first derivative of A(e^{-x}-e^{-x}x) is A(e^{-x}x-2e^{-x})

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

A (e^{- x} x - 2 e^{- x})

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

= A (\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}

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

Simplify

= A (e^{- x} x - 2 e^{- x})

y = 8 x arccos (x - 1), at x = 1

\int_{t}^{1} (\frac{1}{x ^{2}}) d x

(t^{2} + 5)^{2} - 7 (t^{2} + 5)

2 x \frac{d y}{d x} - 8 y = x^{- 8}

\frac{d y}{d x} = - \frac{x}{y}, y (0) = 1

What is the derivative of A(e^{-x}-e^{-x}x) ?
The derivative of A(e^{-x}-e^{-x}x) is A(e^{-x}x-2e^{-x})
What is the first derivative of A(e^{-x}-e^{-x}x) ?
The first derivative of A(e^{-x}-e^{-x}x) is A(e^{-x}x-2e^{-x})