Finding the derivative of $r = \left(\frac{m^2}{a}\right)\left(\frac{1}{b}-\frac{m}{c}\right)$

Question

I needed some help finding the derivative of the following at $m=15$ $$r = \left(\frac{m^2}{a}\right)\left(\frac{1}{b}-\frac{m}{c}\right)$$

Where $a,b,c$ are constants

I have no idea where to start. Can someone please point me in the correct direction?

Thanks!

Answer 1

$$r =\frac{m^2}{a}\left(\frac{1}{b}-\frac{m}{c}\right)$$ $$r' =\frac{2m}{a}\left(\frac{1}{b}-\frac{m}{c}\right)+\frac{m^2}{a}\left(-\frac{1}{c}\right)$$ $$r'(15) =\frac{2\cdot 15}{a}\left(\frac{1}{b}-\frac{15}{c}\right)+\frac{15^2}{a}\left(-\frac{1}{c}\right)$$ $$r'(15) =\frac{30}{a}\left(\frac{1}{b}-\frac{15}{c}\right)+\frac{225}{a}\left(-\frac{1}{c}\right)$$