Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2010MathematicsDifferentiationActual

If x=t^2, y=t^3 , then what is d^2 y d x^2 equal to?

Options

  1. A1
  2. B3 2 t
  3. C3 4 t
  4. D3 2

Correct answer

C. 3 4 t

Step-by-step solution

aligned & x=t^2, y=t^3 & d x d t =2 t, d y d t =3 t^2 & d y d x = d y / d t d x / d t = 3 t^2 2 t = 3 2 t aligned aligned & Also, d^2 y d x^2 = 3 2 1 d t d x & = 3 2 1 2 t = 3 4 t 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