What is the derivative of-2(4e^{-x^2}x^3-6e^{-x^2}x) ?

The derivative of-2(4e^{-x^2}x^3-6e^{-x^2}x) is -2(-8e^{-x^2}x^4+24e^{-x^2}x^2-6e^{-x^2})

What is the first derivative of-2(4e^{-x^2}x^3-6e^{-x^2}x) ?

The first derivative of-2(4e^{-x^2}x^3-6e^{-x^2}x) is -2(-8e^{-x^2}x^4+24e^{-x^2}x^2-6e^{-x^2})

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derivative of

- 2 (4 e^{- x^{2}} x^{3} - 6 e^{- x^{2}} x)

- 2 (- 8 e^{- x^{2}} x^{4} + 24 e^{- x^{2}} x^{2} - 6 e^{- x^{2}})

Solution steps

\frac{d}{d x} (- 2 (4 e^{- x^{2}} x^{3} - 6 e^{- x^{2}} x))

Take the constant out:

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

= - 2 \frac{d}{d x} (4 e^{- x^{2}} x^{3} - 6 e^{- x^{2}} x)

Apply the Sum/Difference Rule:

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

= - 2 (\frac{d}{d x} (4 e^{- x^{2}} x^{3}) - \frac{d}{d x} (6 e^{- x^{2}} x))

\frac{d}{d x} (4 e^{- x^{2}} x^{3}) = 4 (- 2 e^{- x^{2}} x^{4} + 3 e^{- x^{2}} x^{2})

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

= - 2 (4 (- 2 e^{- x^{2}} x^{4} + 3 e^{- x^{2}} x^{2}) - 6 (- 2 e^{- x^{2}} x^{2} + e^{- x^{2}}))

Expand

4 (- 2 e^{- x^{2}} x^{4} + 3 e^{- x^{2}} x^{2}) - 6 (- 2 e^{- x^{2}} x^{2} + e^{- x^{2}}) : - 8 e^{- x^{2}} x^{4} + 24 e^{- x^{2}} x^{2} - 6 e^{- x^{2}}

= - 2 (- 8 e^{- x^{2}} x^{4} + 24 e^{- x^{2}} x^{2} - 6 e^{- x^{2}})

ln^{2} (2 x)

x \to 1 lim (\frac{∣ x - 1 ∣}{1 - x})

\frac{x ^{2} + 4 x + 3}{x}

\int \frac{1}{36 e ^{- 9 x} + e ^{9 x}} d x

\frac{\partial}{\partial y} (x - y)

What is the derivative of-2(4e^{-x^2}x^3-6e^{-x^2}x) ?
The derivative of-2(4e^{-x^2}x^3-6e^{-x^2}x) is -2(-8e^{-x^2}x^4+24e^{-x^2}x^2-6e^{-x^2})
What is the first derivative of-2(4e^{-x^2}x^3-6e^{-x^2}x) ?
The first derivative of-2(4e^{-x^2}x^3-6e^{-x^2}x) is -2(-8e^{-x^2}x^4+24e^{-x^2}x^2-6e^{-x^2})