Select the appropriate hint from the hint basket and fill in the blank spaces in the following paragraph. [Activity]
"Let f(x)= `sin x` and g(x)= log x then f[g(x)]= ------- and g[f(x)]= ----. Now f'(x)= -------and g'(x)= -------. The derivative of `f[g(x)]` w.r.t.x in terms of f and g is ------. Therefore `(d)/(dx) [f[g(x)]]`= ------- and `[(d)/(dx) [f[g(x)]]]_(x=1)`= ------
The derivative of g [f(x)] w.r.t. x in terms of f and g is -----. Therefore `(d)/(dx) [g[f(x)]]`= ------and `[(d)/(dx) [g[f(x)]]]_(x= (pi)/(3))`= ----"
Hind basket : {f'[g(x)].g'(x), `(cos (log x))/(x)`, 1, g'[f(x)].f'(x), `cot x`, `sqrt3, sin (log x), log (sin x), cos x, (1)/(x)`}

Answer

`sin (log x), log (sin x), cos x, (1)/(x), f'[g(x)].g' (x), (cos (log x))/(x), 1, g' [f(x)].f' (x), cot x, sqrt3`