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

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

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

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

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

A (4 e^{- 2 x} x - 4 e^{- 2 x})

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Expand

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

= A (4 e^{- 2 x} x - 4 e^{- 2 x})

\frac{d}{d x} ((6 x^{2} + 7 x)^{4})

\int e^{2 x + 4} - 6 x d x

x^{2} \frac{d y}{d x} = \frac{5 x ^{2} - x - 3}{( x + 1 ) ( y + 1 )}

\int 9 x^{8} e^{4 x^{9}} d x

\frac{\partial}{\partial x} (x^{2} ln (3 y - 5))

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