Question

Find y' if x = cos(y).

Answer 1

1. Solve for y (complex solution)

y=−iln(x2−1​+x)+2πn1​, n1​∈Z

y=−iln(−x2−1+x)+2πn2​, n2​∈Z

2. Solve for y (Easier)

y=−arccos(x)+2πn1​, n1​∈Z

y=arccos(x)+2πn2​, n2​∈Z, ∣x∣≤1