What is the derivative of a(2e^{-x}x-e^{-x}x^2) ?

The derivative of a(2e^{-x}x-e^{-x}x^2) is a(e^{-x}x^2-4e^{-x}x+2e^{-x})

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

The first derivative of a(2e^{-x}x-e^{-x}x^2) is a(e^{-x}x^2-4e^{-x}x+2e^{-x})

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\frac{d}{d x} (a (2 e^{- x} x - e^{- x} x^{2}))

a (e^{- x} x^{2} - 4 e^{- x} x + 2 e^{- x})

Solution steps

\frac{d}{d x} (a (2 e^{- x} x - e^{- x} x^{2}))

Take the constant out:

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

= a \frac{d}{d x} (2 e^{- x} x - e^{- x} x^{2})

Apply the Sum/Difference Rule:

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

= a (\frac{d}{d x} (2 e^{- x} x) - \frac{d}{d x} (e^{- x} x^{2}))

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

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

= a (2 (- e^{- x} x + e^{- x}) - (- e^{- x} x^{2} + 2 e^{- x} x))

Expand

2 (- e^{- x} x + e^{- x}) - (- e^{- x} x^{2} + 2 e^{- x} x) : e^{- x} x^{2} - 4 e^{- x} x + 2 e^{- x}

= a (e^{- x} x^{2} - 4 e^{- x} x + 2 e^{- x})

x \to 1 lim (9 x - 5)

\frac{d}{d x} (x^{3} + x^{2} - 6 x)

h (x) = 2 x (6 x - 18)^{6}

\int \frac{7 - 4 x ^{3} + 6 x ^{6}}{x ^{6}} d x

3 y^{^{''}} - 8 y^{^{'}} - 3 y = 0, y (0) = - 9, y^{^{'}} (0) = 8

What is the derivative of a(2e^{-x}x-e^{-x}x^2) ?
The derivative of a(2e^{-x}x-e^{-x}x^2) is a(e^{-x}x^2-4e^{-x}x+2e^{-x})
What is the first derivative of a(2e^{-x}x-e^{-x}x^2) ?
The first derivative of a(2e^{-x}x-e^{-x}x^2) is a(e^{-x}x^2-4e^{-x}x+2e^{-x})