If `f(x)` is differentiable then `f'(x)=`

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

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

f:R rarr R,f(x) is differentiable such that f(x)=k(x^(5)+x).(kne0) Then f(x) is

If f(x) is differentiable function and f(x)=x^(2)+int_(0)^(x) e^(-t) (x-t)dt ,then f)-t) equals to

f:R rarr R,f(x) is differentiable such that f(x)=k(x^(5)+x).(kne0) Then f(x) is increasing . In the above question k can take value,

f:R rarr R,f(x) is differentiable such that f(f(x))=k(x^(5)+x),k!=0). Then f(x) is always increasing (b) decreasing either increasing or decreasing non-monotonic

If f(x) is differentiable at x=a, then lim_(x toa)(x^2f(a)-a^2f(x))/(x-a) is equal to

The contrapositive of statement: If f(x) is continuous at x=a then f(x) is differentiable at x=a

If f (x) is odd and differentiable , then f'(x) is

A function f:R rarr R satisfies the equation f(x+y)=f(x)f(y) for allx,y in R and f(x)!=0 for all x in R .If f(x) is differentiable at x=0 .If f(x)=2, then prove that f'(x)=2f(x) .