I am stuck with proving the following statement. In fact, I am proving another assumption, and the proof of this would help me to proceed.
Assume that $f_1$ and $f_2$ are differentiable on the interval $(a,b)$. Then define $f=f_1+f_2$. Show that $f$ is differentiable on any point in that interval. So I guess I need to prove that the sum of two differentiable functions on an interval is differentiable
My attempt: I wanted to prove it from definition, writing
Then I can write them under the same limit, but then I cannot proceed. Would be thankful if anyone helped me with it.