Question

differentiate with respect to x y=(1+(1+(1+x)^1/2)^1/2)^1/2)

Answer 1

Chain rule again...

(1/2)((1+(1+(1+x)^1/2)^(1/2))^1/2)^(-1/2)(1/2)(1+(1+x)^(1/2))^(-1/2)(1/2)(1+x)(-1/2)

If my parentheses are in order, that should be fine.

We just bring down the outer power, reduce the exponent by one, then do the same for the bit in the next ourtermost parentheses and multiply them together, etc.