Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202120 Aug 2021Morning ShiftMathematicsDifferentiationActual

If y = tan - 1 a x - b b x + a , then y ' =

Options

  1. A1 1 + x 2 + a 2 a 2 + b 2
  2. B1 1 + x 2
  3. C1 1 + a x - b b x + a 2
  4. Db x + a 1 + ( a x - b ) 2

Correct answer

B. 1 1 + x 2

Step-by-step solution

y = tan - 1 a x - b b x + a d y d x = 1 1 + a x - b b x + a 2 × b x + a a - a x - b b b x + a 2 d y d x = 1 1 + a x - b b x + a 2 × a 2 + b 2 b x + a 2 d y d x = a 2 + b 2 b 2 x 2 + a 2 + 2 a b x + a 2 x 2 + b 2 - 2 a b x = a 2 + b 2 x 2 a 2 + b 2 + a 2 + b 2 d y d x = 1 x 2 + 1

Practice Differentiation on Quantrex Academy →

More from Differentiation

The domain of the derivative of the function f(x)= x 1+|x| is 2025If x= 2^ cosec ⁻¹ t and y= 2^ ⁻¹ t ,|t| 1 then d y d x = 2025If (a+ 2 b x)(a- 2 b y)=a^2-b^2 where a>b>0 , then at ( 4 , 4 ) , dy dx = 2025If x y - y x =0 , then d y d x = 2025If y = ( _ x x )^ x , then dy dx = 2025If f(x)=x^ Sec ⁻¹ x , then f^ (2)= 2025If y= x^4 3 x-5 (x^2-3 )(2 x-3) , then ( d y d x )_ x=2 = 2025If x^2+y^2+ y=4 , then the value of d^2 y d x^2 at x=-2 is 2025 Full Differentiation list All AP EAMCET PYQs