Find f'(x) ab -initio when `f(x) = 1/x`

Find f' (x) when f(x) = sin^-1(1/sqrt(x+1))

Find f' (x) when f(x) = 2^(cos^2x)

Find f(x) when it is given by f(x)=max{x^(3),x^(2),(1)/(64)},AA x in [0, oo).

Find lim_(x to 0)f(x) , when f(x) = (5x + 2) .

Find the value of 'A', if the function f at (x) = 0 is continuous when f(x) ={((1-cos Ax)/(x sin x)),(1/2):}, ((x ne 0),(x =0))

For x inR - {1} , the function f(x ) satisfies f(x) + 2f(1/(1-x))=x . Find f(2) .

Find the domain of function f(x)= (1)/([abs(x-1)]+[abs(7-x)]-6) where [*] denotes the greatest integral function .

Find the domain of continuity of the following functions: f(f(x)), where f (x) = 1/(x-1)

Find lim_(x rarr 1)f(x) where f(x)= {(x^2-1,xle1),(-x^2-1,x>1):}

find derivative, find f' (2) when f(x) = 5^(3x)