If `y=(x+(1)/(x+(1)/(x+ . . .oo)))` find `(dy)/(dx)`, the rhs being a valid expression.

Find (dy)/(dx) when y=x^y .

Find, (dy)/(dx) when y=x^x .

If y=sin^(-1)((2x)/(1+x^(2))) , then find (dy)/(dx)

If y=x+frac[1][x+frac[1][x+...infty]] find frac[dy][dx] , the rhs being a valid expression.

If y=sqrt(x+sqrt(x+sqrt(x+...oo))) , then find (dy)/(dx) .

If y=(sinx)^(x)+sin^(-1)sqrt(x) , then find (dy)/(dx) .

If y=(log x)^(cos x)+(x^2+1)/(x^2-1) find (dy)/(dx) .

If y=sec^(-1)((x^(2)+1)/(x^(2)-1)) , then find (dy)/(dx) . Here f^(-1)(x) expression is of the form (x^(2)+a^(2))/(x^(2)-a^(2)) , so we substitute x=tan theta and then use suitable trigonometrical formula to write it in simplest form and then differentiate