Question

.....Solve this pleaseeeeeeeeeeeee​

Answer 1

Answer:

1 / 2

Step-by-step explanation:

To find-----> Differentiate

tan⁻¹ [ { √(x² + 1 ) - 1 } / x ] with respect to tan⁻¹ x .

Solution----->

1) Plzzz see the attachment .

2) First we find differential of first function for this , we substitute x = tanθ

=> tan⁻¹x = tan⁻¹ ( tanθ )

=> tan⁻¹ x = θ

3) In sixth step we use the formula

1 + tan²θ = Sec²θ

4) In 8th step we used ,

SecA = 1 / CosA and tanA = SinA / CosA

5) In 11th step we used two formulee,

CosA = 1 - 2 Sin²( A/2 )

SinΑ = 2 Sin ( A / 2 ) Cos ( A / 2 )

6) In 14th step we used ,

tanθ = Sinθ / Cosθ

7) In 17th step we used formula of differentiation

d/dx ( tan⁻¹ x ) = 1 / ( 1 + x² )

8) Now we differentiate second function

9) then we find the answer by dividing differentiation of first function by that of second function .