What is (\partial)/(\partial x)(e^{-r(x-ct)^2}) ?

The answer to (\partial)/(\partial x)(e^{-r(x-ct)^2}) is -2e^{-r(x-ct)^2}r(x-ct)

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(\partial)/(\partial x)(e^{-r(x-ct)^2})

\frac{\partial}{\partial x} (e^{- r (x - c t)^{2}})

- 2 e^{- r (x - c t)^{2}} r (x - c t)

Solution steps

\frac{\partial}{\partial x} (e^{- r (x - c t)^{2}})

Treat

c, r, t

as constants

Apply the chain rule:

e^{- r (x - c t)^{2}} \frac{\partial}{\partial x} (- r (x - c t)^{2})

= e^{- r (x - c t)^{2}} \frac{\partial}{\partial x} (- r (x - c t)^{2})

\frac{\partial}{\partial x} (- r (x - c t)^{2}) = - 2 r (x - c t)

= e^{- r (x - c t)^{2}} (- 2 r (x - c t))

Simplify

= - 2 e^{- r (x - c t)^{2}} r (x - c t)

\frac{d}{d x} (\frac{3 - 5 x - x ^{2}}{x ^{2} - 6})

x \to 0 lim (\frac{x}{x ^{2} - 5 x})

x \to \infty + lim (x^{2})

y = x^{2} - 2 x - 4

cos (x^{3})

What is (\partial)/(\partial x)(e^{-r(x-ct)^2}) ?
The answer to (\partial)/(\partial x)(e^{-r(x-ct)^2}) is -2e^{-r(x-ct)^2}r(x-ct)