If y=f(x), p= d y d x ; q= d^2 y d x^2 then d^2 x d y^2 is equal to

Step-by-step solution

Given p = dy dx , we have dx dy = 1 p = p⁻¹ . Differentiating both sides with respect to y using the chain rule: d^2x dy^2 = d dy ( p⁻¹ ) = d dx ( p⁻¹ ) dx dy d^2x dy^2 = -p⁻² dp dx 1 p Since p = dy dx , then dp dx = d^2y dx^2 = q . Substituting these values: d^2x dy^2 = - 1 p^2 q 1 p = - q p^3 Answer: - q p^3