Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2022MathematicsDifferentiationActual

If d d x ( 1+x^4+x^8 1-x^2+x^4 )=a x+b x^3 , then which one of the following is correct?

Options

  1. Aa=b
  2. Ba=2 b
  3. Ca+b=0
  4. D2 a=b

Correct answer

D. 2 a=b

Step-by-step solution

aligned & Let f(x)= x^8+x^4+1 x^4-x^2+1 & = x^8+2 x^4+1-x^4 x^4-x^2+1 = (x^4+1 )^2- (x^2 )^2 (x^4-x^2+1 ) & = (x^4-x^2+1 ) (x^4+x^2+1 ) x^4-x^2+1 & f(x)=x^4+x^2+1 & f^ (x)=4 x^3+2 x=a x+b x^3 & a=2, b=4 b=2 a aligned

Practice Differentiation on Quantrex Academy →

More from Differentiation

Passage: Let (e^y )^x-y=0 , where y is a function of x whose domain is (0,10] . Question: What is dy dx equal to, given that y=y₀ when x=1 ? 2026If [4] y =x+ x^2+4 , then what is x^2+4 , dy dx equal to ? 2026Passage: Let (e^y )^x-y=0 , where y is a function of x whose domain is (0,10] . Question: What is dy dx equal to ? 2026For the following two (02) items: Consider the function f(x) = cases 4(5^x), & x What is f'(-1) equal to? 2025Consider the following for the two (02) items that follow: Let x = - and y = ^4 - ^4 . What is ( dy dx )^2 equal to? 2025Consider the following for the two (02) items that follow: Let (x+y)^ p+q = x^p y^q , where p , q are positive integers. The derivative of y with respect to x 2025Consider the following for the two (02) items that follow: Let y = ⁻¹ (x - 4x^3 27 ) . What is dy dx equal to? 2025For the following three (03) items: Let y = f(x) = x ⁻¹ x 1 - x^2 + 1 - x^2 . If x = , then what is dy dx equal to? 2025 Full Differentiation list All NDA PYQs