let f be a function satisfying f(x+y)=f(x) + f(y)

and f(x)=x*2g(x)      ( here 2 is in its exponential form)   x,y belonging to R

where g(x) is a continous function then

f`(x)=

a) g`(x)

b)g(0)

c)g(0) + g(x)

d)0                                                          thank you

I think the ans is 0,bcoz

limh0 f(x+h)-f(x)/h=limh0 f(h)/h=limh0 h.g(h)=0

Hence,f'(x)=0

answer is correct but i didnt understand the explaination

after the first principle how did you get lim h tending to0  f(h)/h

pls explain it in detail

can you explain the ans with the help of conditions given in the problem

see

limh0 f(x+h)-f(x)/h= limh0 [f(x) + f(h) - f(x)]/h   (as it is given that f(x+y) = f(x) + f(y)

 = limh0  f(h)/h          now f(h) = h^2g(h) (bcoz it's given that f(x) = x^2g(x))

=> limh0  f(h)/h  =  limh0 hg(h) =  0

hope now u have understood

thank you friends

thanks a lot