If y=f(x) is a thrice differentiable function and a bijection then that d^2 x d y^2 ( d y d x )^3+ d^2 y d x^2 =

Step-by-step solution

Given, y=f(x) is differentiable and bijective function. Now, d x d y = 1 ( d y d x ) d d y ( d y d x )= d d y ( d y d x )⁻¹ aligned & d^2 x d y^2 = d d y ( ( d y d x )⁻¹ ) d x d y & d^2 x d y^2 =- ( d y d x )⁻² d^2 y d x^2 ( d y d x )⁻¹ & d^2 x d y^2 ( d y d x )^3+ d^2 y d x^2 =0 aligned