Hey StackExchange I have a question for you guys. I have a homework problem and my first intuition is to use the quotient rule (or re-write the expression to use the product rule) but the product/quotient rules haven't been covered yet so I feel like they wouldn't expect me to use them. Perhaps you guys could show me where to start. The problem is as follows:
If $F(X) = \frac{5x}{1 + x^2}$, find $F'(2)$ and use it to find an equation of the tangent line to the curve $y = \frac{5x}{1+x^2}$ at the point $(2, 2)$.
I know I just have to calculate the derivative and plug in numbers, my question just concerns alternatives to the quotient rule.
Best Answer
I suspect that they intend for you to find $$\lim_{x\to 2}\frac{F(x)-F(2)}{x-2},$$ which is the limit definition of $F'(2).$