Question

d/dx tan⁻¹(x+a/1-xa)=.......... (x, a ∈ R⁺, xa > 1) ,Select Proper option from the given options.
(a) 1/1+x²
(b) 1/1+a²
(c) 1/1+x² + 1/1+a²
(d) 1/1+x²a²

Answer 1

Tan^-1(4√x/1-4x)=y

Take x to be tan^2p÷4, then 4√x becomes tanp÷2 and 1-4x becomes,1-tan^2p. Then the whole expression now becomes,tan^-1(2tanp/1-tan^2 p) this gives you tan^-1(tan2p) which is equal to 2p. so now the question is simplified. Y=2p,but p=1/2 tan^-1(4x). Dy/dx= 2(1/1+16x^2).

Answer 2

Answer:

1/1+x^2 option A this is correct answer