If $y=\frac{1}{3u}\frac{du}{dx}$, find $\frac{dy}{dx}.$

Question

My thoughts:

Differentiating with respect to x gives:

$\frac{dy}{dx}=\frac{1}{3u}\frac{d^2u}{dx^2}-\frac{1}{3u^2}\frac{du}{dx}$

However, it should be:

$\frac{dy}{dx}=\frac{1}{3u}\frac{d^2u}{dx^2}-\frac{1}{3u^2}(\frac{du}{dx})^2$

Could someone explain this?

Yes, the extra du/dx comes from chain rule on u. – Benjamin Wang Feb 12 '21 at 12:54 — Benjamin Wang, Feb 12 '21 at 12:54
Ah yes, obvious now that you say it. Thank you! – Jamminermit Feb 12 '21 at 12:58 — Jamminermit, Feb 12 '21 at 12:58

Z Ahmed · Accepted Answer · 2021-02-12T14:55:40.637

2

$$y=\frac{1}{3u}\frac{du}{dx}$$ D.w.t. $x$ $$\frac{dy}{dx}=\frac{-1}{3u^2}\left(\frac{du}{dx}\right)^2+\frac{1}{3u}\frac{d^2u}{dx^2}$$ When you differentiate $u$, $du/dx$ will multiply.

edited Feb 12 '21 at 14:55

answered Feb 12 '21 at 12:58

Z Ahmed

43,235

Oh! yes thanks. – Z Ahmed Feb 12 '21 at 14:55

If $y=\frac{1}{3u}\frac{du}{dx}$, find $\frac{dy}{dx}.$

1 Answers1