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})

\int_{1}^{e^{3}} x^{2} ln (x) d x

x \to 5 lim (123)

\frac{d}{d x} (\frac{1}{3} x^{\frac{1}{2}} - x^{\frac{3}{2}})

(- 1 x y^{2} + 2 y) d x + (- 1 x^{2} y + 2 x) d y = 0

4 sec (θ)

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})