I have this question :

Find out derivative : y = √(x √(x + sineⁿ))

{ I use : n = x }

I named : u = x + sineⁿ

so,

y' = ½ (x + √y)ª · (1 + ½ · uª)· u'

{ I use : a = - ½ }

And : u' = 1 + (sineⁿ)'

But I have many problems with the last number. I Think it would be something like this :

Ln y = x Ln e

1/y· y' = x/sine· sine' + Ln sine

y'/y = (x cose + sine · Ln sine) / sine

y' = sineⁿ‾¹ (x cose + sine · Ln sine)

Finally I think there is something wrong, cause at last, I find out a very complex expression...