Ques- Is it reosonable to assert that the product F(x)=f(x)g(x) has no derivative at x=xo if:

the function f(x) has dervative at point xo,and the function #(x) has no derivative at this point ?

Dear Raiyan

F(x)=f(x)g(x)

F`(x)=f`(x)g(x)+f(x)g`(x)   (Using the chain rule)

at point x=x₀

F`(x<sub>0</sub>)=f`(x₀)g(x₀)+f(x₀)g`(x₀)

But  g`(x<sub>0</sub>) does not exist .so F`(x₀) al so does not exist.

ALL THE BEst

ABhinav batra