Question

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

(a) u’vw + uv’w + uvw’

(b) uvw + uv’w’ + u’v’w’

(c) u’v’w + uv’w’ + u’vw’

(d) uv’w’ + u’v’w’ + uvw

This question was addressed to me in an internship interview.

The above asked question is from Limits and Derivatives of Several Variables topic in portion Partial Differentiation of Engineering Mathematics

Answer 1

Right answer is (a) u’vw + uv’w + uvw’

The best explanation: \(\frac{d(uvw)}{dx}=u\frac{d(uvw)}{dx}+vw\frac{d(u)}{dx}=u[v\frac{d(w)}{dx}+w\frac{d(v)}{dx}]+vw\frac{d(u)}{dx}\)=u’vw+uv’w+uvw’