Question

\(\frac{d(\frac{u}{v})}{dx}\) is where u, v are the functions of x

(a) ^v’u’ – uv ⁄ v^2

(b) ^vu’ – uv’ ⁄ v^2

(c) ^vu – u’v’ ⁄ v^2

(d) 0

I have been asked this question in homework.

Query is from Limits and Derivatives of Several Variables in section Partial Differentiation of Engineering Mathematics

Answer 1

Right answer is (b) ^vu’ – uv’ ⁄ v^2

The explanation is: \(\frac{d(\frac{u}{v})}{dx}=u\frac{d(\frac{1}{v})}{dx}+\frac{1}{v}\frac{d(u)}{dx}=-\frac{u}{v^2}\frac{d(v)}{dx}+\frac{1}{v}\frac{d(u)}{dx}=\frac{vu’-uv’}{v^2}\)