What is (d^4)/(dx^4)(e^{-x^2}) ?

The answer to (d^4)/(dx^4)(e^{-x^2}) is -2(-8e^{-x^2}x^4+24e^{-x^2}x^2-6e^{-x^2})

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(d^4)/(dx^4)(e^{-x^2})

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

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

Solution steps

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

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

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

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

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

\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)

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

\frac{d}{d x} (- 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}})

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

What is (d^4)/(dx^4)(e^{-x^2}) ?
The answer to (d^4)/(dx^4)(e^{-x^2}) is -2(-8e^{-x^2}x^4+24e^{-x^2}x^2-6e^{-x^2})