(i) if `f(x) = 5^(g(x))` and `g(x) = int_(2)^(x^(2))(t)/(ln(1+t^(2)))` dt, then find the value of `f'(sqrt(2))`.
(ii) The value of `lim_(xrarr0) ((d)/(dx)int_(0)^(x^(2)) sqrt(cost)dt)/(1-sqrt(cosx))`
(iii) Find the slope of the tangent to the curve , `y = int_(x)^(x^(2)) cos^(-1)t^(2)dt` at `x = (1)/(4sqrt(2))`\

Answer

(i) `4sqrt(2)` , (ii) `12` , (iii) `((4sqrt(8))/(3)- (1)/(4)) pi`