Q. 205.0( 1 Vote )

If y =(tan–1x)2, show that

Answer :

Given: y =(tan–1x)2


To show:


given y =(tan–1x)2


Now applying first derivative with respect to x, we get



Now applying the power rule of differentiation, we get



And we know differentiation of , substituting this in above equation, we get



Now applying second derivative with respect to x, we get



Taking out the constant term, we get



Now applying the quotient rule of differentiation, we get



And we know differentiation of , substituting this in above equation, we get



Now applying the sum rule of differentiation, we get





Now we will consider the LHS,



Now we will substitute the values from equation (i) and (ii)in above equation, we get



⇒=(2[1-2x(tan-1x)])+2x(2(tan-1x))


⇒=(2[1-2x(tan-1x)]+ 2x(tan-1x))


⇒=2=RHS


Hence proved



Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
All About Faraday's lawAll About Faraday's lawAll About Faraday's law55 mins
Revision Class | All Formulas of ElectrodynamicsRevision Class | All Formulas of ElectrodynamicsRevision Class | All Formulas of Electrodynamics63 mins
Know all about InfertilityKnow all about InfertilityKnow all about Infertility39 mins
Get to know all about Immune SystemGet to know all about Immune SystemGet to know all about Immune System60 mins
Know all about Colligative PropertiesKnow all about Colligative PropertiesKnow all about Colligative Properties50 mins
Know All About Types of RelationsKnow All About Types of RelationsKnow All About Types of Relations53 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

If y = sin-1 x, show that

Mathematics - Board Papers

If x = t2, y = t3, then is

Mathematics - Exemplar

If prove that

Mathematics - Exemplar

If y =(tan–1x)2, show that

Mathematics - Board Papers