Question

Evaluate the differentiation of \(tan^{-1}\frac{cos(x)-sin(x)}{cos(x)+sin(x)}\)

(a) tan^-1⁡x

(b) 1

(c) 0

(d) -1

The question was asked by my school teacher while I was bunking the class.

I'd like to ask this question from Limits and Derivatives of Several Variables topic in section Partial Differentiation of Engineering Mathematics

Answer 1

The correct option is (b) 1

For explanation: \(tan^{-1}\frac{cos(x)-sin(x)}{cos(x)+sin(x)}=tan^{-1}tan(x)=x\)

Hence

\(\frac{d}{dx}tan^{-1}\frac{cos(x)-sin(x)}{cos(x)+sin(x)}=1\)