if `f(x)={ lnx, 0=1`

Find the left and right hand derivative of the following function at given point: f(x)=|lnx|a t\ x=1

Find the greatest and the least values of the following functions on the indicated intervals : f(x) = x-2lnx on [1,e]

y=e^(x)lnx

f(x)=x^(2)+lnx

Find fog and gof if: f(x)=e^(x),g(x)=lnx

Let f be a real-valued function defined on interval (0,oo),by f(x)=lnx+int_0^xsqrt(1+sint).dt. Then which of the following statement(s) is (are) true? (A). f"(x) exists for all in (0,oo)." " (B). f'(x) exists for all x in (0,oo) and f' is continuous on (0,oo), but not differentiable on (0,oo)." " (C). there exists alpha>1 such that |f'(x)|<|f(x)| for all x in (alpha,oo)." " (D). there exists beta>1 such that |f(x)|+|f'(x)|<=beta for all x in (0,oo).