Let f(x)=cos(cos(cos(cos(cos(cos(cos(cosx))))))), and suppose that the number j satisfies the equation j=cosj. If f′(j) can be expressed as a polynomial in j as
f′(j)=aj8+bj6+cj4+dj2+e
where a, b, c, d and e are integers. Then find the value of ∣a∣+∣b∣+∣c∣+∣d∣+∣e∣.
Notation: f′(⋅) denotes the first derivative of the function f(⋅).
For more problems on calculus, click here.