What is (\partial)/(\partial x)(1/a e^{-(x/a)^2}) ?

The answer to (\partial)/(\partial x)(1/a e^{-(x/a)^2}) is -(2e^{-\frac{x^2)/(a^2)}x}{a^3}

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(\partial)/(\partial x)(1/a e^{-(x/a)^2})

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

- \frac{2 e ^{- \frac{x ^{2}}{a ^{2}}} x}{a ^{3}}

Solution steps

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

Take the constant out:

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

= \frac{1}{a} \frac{\partial}{\partial x} (e^{- (\frac{x}{a})^{2}})

Apply the chain rule:

e^{- (\frac{x}{a})^{2}} \frac{\partial}{\partial x} (- (\frac{x}{a})^{2})

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

\frac{\partial}{\partial x} (- (\frac{x}{a})^{2}) = - \frac{2 x}{a ^{2}}

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

Simplify

\frac{1}{a} e^{- (\frac{x}{a})^{2}} (- \frac{2 x}{a ^{2}}) : - \frac{2 e ^{- \frac{x ^{2}}{a ^{2}}} x}{a ^{3}}

= - \frac{2 e ^{- \frac{x ^{2}}{a ^{2}}} x}{a ^{3}}

f (x) = 8 x^{2} + 3 x, at x = - 45

\frac{d y}{d x} = 2 sec^{2} (x) e^{2 y}, y (0) = 0

x \to 3 lim (\frac{x - 2 - 1}{x - 3})

\int \frac{1}{x + 4 + x + 3} d x

y^{^{''}} + 4 y^{^{'}} + 8 y = 4 cos (2 t) + 2 sin (2 t)

What is (\partial)/(\partial x)(1/a e^{-(x/a)^2}) ?
The answer to (\partial)/(\partial x)(1/a e^{-(x/a)^2}) is -(2e^{-\frac{x^2)/(a^2)}x}{a^3}