Question

Value of ^d⁄dx⁡ [(1 + xe^x}{1-Cos(x))].

(a) \(\frac{(1-Sin(x))(1+x) e^x + Cos(x)(1+xe^x)}{[1-Cos (x)]^2}\)

(b) \(\frac{(1-Cos(x))(1+x) e^x + Sin(x)(1+xe^x)}{[1-Cos (x)]^4}\)

(c) \(\frac{(1-Cos(x))(1+x) e^x + Sin(x)(1+xe^x)}{[1-Cos (x)]^2}\)

(d) \(\frac{(1-Cos(x))(1+x) e^x – Sin(x)(1+xe^x)}{[1-Cos (x)]^2}\)

This question was addressed to me in an interview.

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

Answer 1

Correct option is (c) \(\frac{(1-Cos(x))(1+x) e^x + Sin(x)(1+xe^x)}{[1-Cos (x)]^2}\)

To explain I would say: \(\frac{d}{dx⁡} (1+xe^x)/(1-Cos(x))\)

\(\frac{d}{dx⁡} (1+xe^x)/(1-Cos(x)) = \frac{(1-Cos(x))(1+x) e^x + Sin(x)(1+xe^x)}{[1-Cos (x)]^2}\)