If `f(x)=e^x and g(x) =log_(e)x,` then find (f+g)(1) and fg(1).

If f(x)=log_(2)xandg(x)=x^(2) then find f(g(2)).

If f(x) =log_(e) (x^(2)-4) then find (df) /(dx)

If f(x) =|log_(e)|x||, then f'(x) equals

If f(x)=log_(x) (log x)," then find "f'(x) at x= e

f(x)=e^x-e^(-x) then find f'(x)

Fill in the blank : If f(x)=e^(x),g(x)=2log_(e)x" and "F(x)=f{g(x)} , then (dF)/(dx) = _________ .

If f(x)=log_(x)(log_(e)x) , then the value of f'(e ) is -

If f(x) = cos(log_e x) , then find the value of f(x) cdot f(y) - 1/2[f(x/y) + f(xy)]

Let g(x) be the inverse of f(x) and f'(x)=1/(1+x^3) . Then find g'(x) in terms of g(x).

If int(e^x-1)/(e^x+1)dx= f(x) +c, then find f(x).