Solving the Shrinking Core Model: Questions & Solutions

[cycling4life]

I have this solution that I don't quite understand

d(ro*pi*D^3/6)/d(t)=-kr*Cao*pi*D^2

from here I would have thought to separate the variables and integrate but the solution says

ro/2* d(D)/d(t) = -kr Cao

I guess my question is how are you able to do that? If you take the derivative of D, why is d(D)/d(t) still left behind?

 

[tiny-tim]

hi cycling4life!

(try using the X² button just above the Reply box )

d(ro*pi*D^3/6)/d(t)
…
I guess my question is how are you able to do that? If you take the derivative of D, why is d(D)/d(t) still left behind?

chain rule … d(D³)/dt = 3D² dD/dt