Question

If y=tan^(-1)⁡(x) , then which one is correct ?

(a) y3 + y1^2 + 4xy2 y1=0

(b) y3 + y1^2 + xy2 y1=0

(c) y3 + 2y1^2 + xy2 y1=0

(d) y2 + 2y1^2 + 4xy2 y1=0

I have been asked this question during an interview.

I need to ask this question from The nth Derivative of Some Elementary Functions topic in portion Differential Calculus of Engineering Mathematics

Answer 1

Right choice is (d) y2 + 2y1^2 + 4xy2 y1=0

The explanation is: y=tan^-1⁡(x)

\(y_1 = \frac{1}{1+x^2}\)

\(y_2 = \frac{-2x}{(1+x^2)^2}\)

\(y_3 = -2[\frac{(1+x^2)^2-4x^2 (1+x^2)}{(1+x^2)^4}]\)

\(y_3 = -2[\frac{1}{1+(x^2)^2}-\frac{(4x^2)}{(1+x^2)^3}]\)

\(y_3+2y_1^2 + 4xy_2 y_1\)=0