If x = a (θ – sin θ), y = a( 1 + cos θ), find d^y/dx^2.

Question

If x = a (θ – sin θ), y = a( 1+cos θ), find d²y/dx².

Answer 1

Here we have to find the double derivative, so to find double derivative we will just differentiate the first derivative once again with a similar method.

Theorem: y and x are given in a different variable that is θ . We can find dy/dx by finding dy/dθ and dx/dθ and then dividing them to get the required thing.

= - cot (θ/2)

⇒ To find f’’ we will differentiate f’ with θ and then divide with equation (2).