What is the derivative of e^{-x^2}(1-2x^2) ?

The derivative of e^{-x^2}(1-2x^2) is 4e^{-x^2}x^3-6e^{-x^2}x

What is the first derivative of e^{-x^2}(1-2x^2) ?

The first derivative of e^{-x^2}(1-2x^2) is 4e^{-x^2}x^3-6e^{-x^2}x

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derivative of

e^{- x^{2}} (1 - 2 x^{2})

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{- x^{2}}, g = 1 - 2 x^{2}

= \frac{d}{d x} (e^{- x^{2}}) (1 - 2 x^{2}) + \frac{d}{d x} (1 - 2 x^{2}) e^{- x^{2}}

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

\frac{d}{d x} (1 - 2 x^{2}) = - 4 x

= (- 2 e^{- x^{2}} x) (1 - 2 x^{2}) + (- 4 x) e^{- x^{2}}

Simplify

(- 2 e^{- x^{2}} x) (1 - 2 x^{2}) + (- 4 x) e^{- x^{2}} : 4 e^{- x^{2}} x^{3} - 6 e^{- x^{2}} x

= 4 e^{- x^{2}} x^{3} - 6 e^{- x^{2}} x

x \to 6 + lim (x^{3} + c x)

f (x) = x + x x

ln (x), 3

x \to 6 lim (h (x))

\frac{1}{( s + 2 ) ^{2}}

What is the derivative of e^{-x^2}(1-2x^2) ?
The derivative of e^{-x^2}(1-2x^2) is 4e^{-x^2}x^3-6e^{-x^2}x
What is the first derivative of e^{-x^2}(1-2x^2) ?
The first derivative of e^{-x^2}(1-2x^2) is 4e^{-x^2}x^3-6e^{-x^2}x