Question: If the function $f(x)$ satisfies the relation $(f(x+y)=yf(x)+f(y))$ with $f(1)=2$, then $\lim_{x\to 1^+}f'(x)$ is:
Domain of function is $(1,\infty)$
I need to find $f'(1)$ to solve this question.
But can't seem to find the solution of the equation.
Now this functional equation is giving me problems.
Solving functions without calculus is often too easy for me but idk why this is hard. Maybe this requires calculus.
Till now I've tried putting $1$ at the places of $x$ and $y$ and then trying to solve which results in $x=1$.
Calculus doesn't help in my case. I tried differentiating which resulted in long differential equation which simplified to $x=1$ again. XD
Thank you.