1. ## Derivative Help

Here is the problem:

Find dA/dD, where A is the surface area of a sphere of diameter D. (The surface area of a sphere of radius r is 4πr2.)

I worked it out and got 4(2pi*r) but that didnt seem to be correct.

Any help is appreciated thanks

2. Originally Posted by elexis10
Here is the problem:

Find dA/dD, where A is the surface area of a sphere of diameter D. (The surface area of a sphere of radius r is 4πr2.)

I worked it out and got 4(2pi*r) but that didnt seem to be correct.

Any help is appreciated thanks
Since your variable is in terms of D. You may need to rewrite your formula accordingly. That is to use $A = 4 \pi (d/2)^2 = ...$ Then you should be able to find dA/dD.

3. In terms of the diameter d, the surface area of a sphere is $4 \pi r^2 = 4 \pi \left(\frac{d}{2}\right)^2 = \pi d^2$.