# Taking the derivative, $d$, of both sides of the equation.

#### operationsres

Suppose that $B(t)$ is a Wiener process. Suppose that the following equation is true:

$B(t)(t + \frac13 B(t)) = B(t)^{0.5}$.

I've conjured this equation out of thin air (it's probably not true) to ask the following question. Does the above identity (assuming it's correct) enable us to write the following:

$dB(t)dt + \frac13 dB(t) = dB(t)^{0.5}$

?

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#### SammyS

Staff Emeritus
Homework Helper
Gold Member
Suppose that $B(t)$ is a Wiener process. Suppose that the following equation is true:

$B(t)(t + \frac13 B(t)) = B(t)^{0.5}$.

I've conjured this equation out of thin air (it's probably not true) to ask the following question. Does the above identity (assuming it's correct) enable us to write the following:

$dB(t)dt + \frac13 dB(t) = dB(t)^{0.5}$

?
In a word, no.

Use the product rule.

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