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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Expand

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

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

x \to 5 lim (2 x^{3} - 3 x^{2} - x - 4)

t y^{^{'}} + y = t

f (x) = \frac{6 x ^{5}}{5} - x + 3 e^{x}

x, at 36

arcsec (5 ln (2 x))

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