What is (\partial)/(\partial x)(te^{(-x^2)/(2t)}) ?

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

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(\partial)/(\partial x)(te^{(-x^2)/(2t)})

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

- e^{- \frac{x ^{2}}{2 t}} x

Solution steps

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

Simplify

t e^{\frac{- x ^{2}}{2 t}} : e^{- \frac{x ^{2}}{2 t}} t

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

Treat

t

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - e^{- \frac{x ^{2}}{2 t}} x

x \to 0 lim (e^{8 π})

\frac{\partial}{\partial z} (2 x + z^{2})

x \to 0 lim ((x + h)^{2} - 1)

\int ln (2 x - 1) d x

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

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