Mathematics - Functions Question with Solution | TestHub

$$f(x+y)=f(x)\times f(y)$$ Differentiate with respect to $x$, treating $y$ as constant $$f^{\prime }(x+y)=f(x)f(y)$$ Putting $x=0$ and $y=x$, we get $f^{\prime }(x)=f^{\prime }(0)f(x);\Rightarrow f^{\prime }(5)=3f(5)=3\times 2=6$