Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET2005MathematicsDifferentiation

Observe the following statements I. f(x)=a x⁴¹+b x⁻⁴⁰ f^ (x) f(x) =1640 x⁻² II. d d x ⁻¹ ( 2 x 1-x^2 )= 1 1+x^2 Which of the following is correct?

Options

  1. AI is true, but II is false
  2. BBoth I and II are true
  3. CNeither I nor II is true
  4. DI is false, but II is true

Correct answer

A. I is true, but II is false

Step-by-step solution

I. aligned & f(x)=a x⁴¹+b x⁻⁴⁰ & f^ (x)=41 a x⁴⁰-40 b x⁻⁴¹ & f^ (x)=1640 a x³⁹+1640 b x⁻⁴² aligned Now, f^ (x) f(x) = 1640 (a x³⁹+b x⁻⁴² ) a x⁴¹+b x⁻⁴⁰ =1640 x⁻² II. aligned & d d x ⁻¹ ( 2 x 1-x^2 ) & = d d x ⁻¹( 2 x) & = d d x 2 x & =2 aligned Statement I is true, but II is false.

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