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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Expand

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

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

\int_{0}^{1} 2 + 5 x^{2} d x

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

(2 x + 1)^{3} + \frac{2}{( 2 x + 1 ) ^{3}}

\frac{\partial}{\partial x} (4 + x + x^{2} Y (x))

\frac{d y}{d x} = x + 2

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