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

The derivative of a(2e^{-2x}x-2e^{-2x}x^2) is a(4e^{-2x}x^2-8e^{-2x}x+2e^{-2x})

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

The first derivative of a(2e^{-2x}x-2e^{-2x}x^2) is a(4e^{-2x}x^2-8e^{-2x}x+2e^{-2x})

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Popular >

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

a (4 e^{- 2 x} x^{2} - 8 e^{- 2 x} x + 2 e^{- 2 x})

Solution steps

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

Take the constant out:

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

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

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

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

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

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

Expand

2 (- 2 e^{- 2 x} x + e^{- 2 x}) - 2 (- 2 e^{- 2 x} x^{2} + 2 e^{- 2 x} x) : 4 e^{- 2 x} x^{2} - 8 e^{- 2 x} x + 2 e^{- 2 x}

= a (4 e^{- 2 x} x^{2} - 8 e^{- 2 x} x + 2 e^{- 2 x})

\int_{- 2}^{4} x + 2 d x

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

y^{^{''}} + 5 y^{^{'}} + 4 y = 2 t e^{3 t}

\int_{0}^{6} 36 - x^{2} d x

x \to 0 + lim (ln (ln (x)))

What is the derivative of a(2e^{-2x}x-2e^{-2x}x^2) ?
The derivative of a(2e^{-2x}x-2e^{-2x}x^2) is a(4e^{-2x}x^2-8e^{-2x}x+2e^{-2x})
What is the first derivative of a(2e^{-2x}x-2e^{-2x}x^2) ?
The first derivative of a(2e^{-2x}x-2e^{-2x}x^2) is a(4e^{-2x}x^2-8e^{-2x}x+2e^{-2x})