Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

The value of
\(\frac{d}{dx}\left [ \tan^{-1}\left \{ \frac{\sqrt{x}(3-x)}{1-3x} \right \} \right ]\)
is

(1) 1/2(1+x)√x

(2) 3/(1+x)√x

(3) 2/(1+x)√x

(4) 3/2(1+x)√x

Solution:

Let y = [ tan-1 {√x(3-x)/(1-3x)}]

Put √x = tan θ

So y = [ tan-1 {tan θ (3 – tan2 θ)/(1 – 3 tan θ2)}]

= [ tan-1 { 3 tan θ – tan3 θ)/(1 – 3 tan θ2)}]

= tan-1 tan 3θ

= 3θ

= 3 tan-1√x

dy/dx = 3/2(1+√x2)√x

= 3/2√x(1+x)

Hence option (4) is the answer.

Was this answer helpful?

 
   

4 (5)

(14)
(3)

Choose An Option That Best Describes Your Problem

Thank you. Your Feedback will Help us Serve you better.

Leave a Comment

Your Mobile number and Email id will not be published. Required fields are marked *

*

*

Ask
Question