## anonymous one year ago The surface area of a right circular cylinder of height 5 feet and radius r feet is given by S(r)=2πrh+2πr2. Find the instantaneous rate of change of the surface area with respect to the radius, r, when r = 6.

1. zepdrix

$\Large\rm S(r)=2\pi r h+2\pi r^2$Hey Camila! :) Have you learned your derivative shortcuts at this point? Or do we have to use the limit definition for the derivative to find our instantaneous rate of change? -_-

2. anonymous

I know how to derive.

3. zepdrix

We're holding the height, h, constant at 5.$\Large\rm S(r)=2\pi r \cdot 5+2\pi r^2$Simplifies our function a little bit, which is nice.$\Large\rm S(r)=10\pi r+2\pi r^2$

4. zepdrix

So apply your power rule to each term, should be pretty straight forward :) Are you getting confused because of all that pi nonsense mixed in?

5. anonymous

Yeah that was the part that confused me.

6. zepdrix

$\Large\rm (10\pi x)'=10\pi(x)'=10\pi (1)$Normal power rule, ignoring the constant coefficients :)

7. anonymous

So I would get 10π+4πr and plug in 6 for r?

8. zepdrix

$\Large\rm S'(r)=10 \pi+4\pi r$Good good good.

9. anonymous

So when I plug that in it would be 34π right?

10. zepdrix

Yayyy good job! *\c:/* Camila <*c:/*

11. anonymous

Haha okay thank you so much!

12. zepdrix

np