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

The answer to (\partial)/(\partial x)(e^{-(x^2)/(4d^2)}) is -(e^{-\frac{x^2)/(4d^2)}x}{2d^2}

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

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

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

Solution steps

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

Treat

d

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{e ^{- \frac{x ^{2}}{4 d ^{2}}} x}{2 d ^{2}}

(1 + cos (t)) (\frac{d y}{d t}) = (1 + e^{- y}) sin (t)

f (x) = (x^{2} + 36) (2 x + 21)

\frac{d y}{d x} = \frac{x}{1 - 4 x ^{2}}

\frac{d ^{3}}{d x ^{3}} ((4 x - 3)^{\frac{1}{2}})

\frac{\partial}{\partial y} (2 x + y^{3})

What is (\partial)/(\partial x)(e^{-(x^2)/(4d^2)}) ?
The answer to (\partial)/(\partial x)(e^{-(x^2)/(4d^2)}) is -(e^{-\frac{x^2)/(4d^2)}x}{2d^2}