What is the derivative of 2e^{-x^2}x-2e^{-x^2}x^3 ?

The derivative of 2e^{-x^2}x-2e^{-x^2}x^3 is 4e^{-x^2}x^4-10e^{-x^2}x^2+2e^{-x^2}

What is the first derivative of 2e^{-x^2}x-2e^{-x^2}x^3 ?

The first derivative of 2e^{-x^2}x-2e^{-x^2}x^3 is 4e^{-x^2}x^4-10e^{-x^2}x^2+2e^{-x^2}

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

4 e^{- x^{2}} x^{4} - 10 e^{- x^{2}} x^{2} + 2 e^{- x^{2}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

2 (- 2 e^{- x^{2}} x^{2} + e^{- x^{2}}) - 2 (- 2 e^{- x^{2}} x^{4} + 3 e^{- x^{2}} x^{2}) : 4 e^{- x^{2}} x^{4} - 10 e^{- x^{2}} x^{2} + 2 e^{- x^{2}}

= 4 e^{- x^{2}} x^{4} - 10 e^{- x^{2}} x^{2} + 2 e^{- x^{2}}

f (x) = 2 x^{- \frac{3}{4}}

3 x - 5 x^{2}

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

\int e^{- s t} (1) d t

f (t) = t^{2} - π^{2}

What is the derivative of 2e^{-x^2}x-2e^{-x^2}x^3 ?
The derivative of 2e^{-x^2}x-2e^{-x^2}x^3 is 4e^{-x^2}x^4-10e^{-x^2}x^2+2e^{-x^2}
What is the first derivative of 2e^{-x^2}x-2e^{-x^2}x^3 ?
The first derivative of 2e^{-x^2}x-2e^{-x^2}x^3 is 4e^{-x^2}x^4-10e^{-x^2}x^2+2e^{-x^2}