Differential calculus?

**fardeen_gen** · June 29th 2008, 07:47 AM

If ω & A are constant then d[ω√(A^2 - x^2)]/dt =?

A) ω/{2√(A^2 - x^2)}
B) -ω/{2√(A^2 - x^2)}
C) -ωx/{√(A^2 - x^2)}
D) None of these

Can u please explain the reasoning too?

**Reckoner** · June 29th 2008, 10:00 AM

Originally Posted by fardeen_gen

If ω & A are constant then d[ω√(A^2 - x^2)]/dt =?

A) ω/{2√(A^2 - x^2)}
B) -ω/{2√(A^2 - x^2)}
C) -ωx/{√(A^2 - x^2)}
D) None of these

Can u please explain the reasoning too?

Are you differentiating with respect to $t$ or with respect to $x$ ?

For $\frac{d}{dt}\left[\omega\sqrt{A^2 - x^2}\right]$ we have

$\frac{d}{dt}\left[\omega\sqrt{A^2 - x^2}\right] = \frac{d}{dt}\left[\omega\left(A^2 - x^2\right)^{1/2}\right]$

$= \frac{\omega}2\left(A^2 - x^2\right)^{-1/2}\frac{d}{dt}\left[A^2 - x^2\right]$

$= \frac{\omega}2\left(A^2 - x^2\right)^{-1/2}\left(-2x\frac{dx}{dt}\right)$

Then you can simplify a bit.

**Mathstud28** · June 29th 2008, 10:25 AM

Originally Posted by Reckoner

Are you differentiating with respect to $t$ or with respect to $x$ ?

For $\frac{d}{dt}\left[\omega\sqrt{A^2 - x^2}\right]$ we have

$\frac{d}{dt}\left[\omega\sqrt{A^2 - x^2}\right] = \frac{d}{dt}\left[\omega\left(A^2 - x^2\right)^{1/2}\right]$

$= \frac{\omega}2\left(A^2 - x^2\right)^{-1/2}\frac{d}{dt}\left[A^2 - x^2\right]$

$= \frac{\omega}2\left(A^2 - x^2\right)^{-1/2}\left(-2x\frac{dx}{dt}\right)$

Then you can simplify a bit.

I believe that

$\frac{d}{dt}\bigg[f(\omega,A,x)\bigg]=0$

Yeah?

**Reckoner** · June 29th 2008, 10:26 AM

Originally Posted by Mathstud28

I believe that

$\frac{d}{dt}\bigg[f(\omega,A,x)\bigg]=0$

Yeah?

Correct, as long as $x$ is constant with respect to $t$ .

**Mathstud28** · June 29th 2008, 10:29 AM

Originally Posted by Reckoner

Correct, as long as $x$ is constant with respect to $t$ .

.........................I know this............................I was pointing something out........in your post.

**fardeen_gen** · June 30th 2008, 05:46 AM

Is the answer 0 then? So D is the correct option, right?

**Reckoner** · June 30th 2008, 08:58 AM

Originally Posted by fardeen_gen

Is the answer 0 then? So D is the correct option, right?

We do not know for sure that $x$ is constant, so you should leave it in a form involving $\frac{dx}{dt}$ . If $x$ happens to be constant the derivative will still work out to be 0.

So in this case, assuming you typed the problem correctly and we are differentiating with respect to $t$ , (D) would be correct.

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