If `f(x) = x + 1`, find `d/(dx)("fof")(x)`.

If f(x)=x+7, and g(x)=x-7, x in R" them find "d/(dx)(fog )(x).

If f(1)=3 , f'(1)=2 , then d/(dx) {logf(e^x+2x)} at x=0 is equal to........

f_n(x)=e^(f_(n-1)(x)) for all n in Na n df_0(x)=x ,t h e n d/(dx){f_n(x)} is (a)(f_n(x)d)/(dx){f_(n-1)(x)} (b) f_n(x)f_(n-1)(x) (c)f_n(x)f_(n-1)(x).......f_2(x)dotf_1(x) (d)none of these

Given f'(1)=1 and (d)/(dx)(f(2x))=f'(x)AA x>0. If f'(x) is differentiable then there exies a number c in(2,4) such that f''(c) equals

If y=f(x) is a differentiable function x such that invrse function x=f^(-1) y exists, then prove that x is a differentiable function of y and (dx)/(dy)=(1)/((dy)/(dx)) where (dy)/(dx) ne0 Hence, find (d)/(dx)(tan^(-1)x) .

If f(x)=(x-1)/(x+1), then find f{f(x)}

If f(x)=|x-3| and g(x)= fof (x), then for x>10,g'(x) is equal to (a)1(b)-1(c)0 (d) none of these