Hi, I'm trying to understand how Differentiation and integral works in practice, and would really appreciate some help interpreting this calculation- If we have a circle with Area A=pi*r^2 1) If i want to find the change in Area with respect to radius then dA/dr= 2pi*r 2) If I'm told that the area of the circle changes with time dA/dt = 0.03 (in)^2/sec And i wanted to find how the radius changes with time, would this then be the right conclusion dr/dt = dr/dA*dA/dt = (1/dA/dr)*dA/dt = 1/(2pi*r)*0.03 So the change in radius with respect to time decreases as the radius increases. So is it correct to leave the expression like this, or should i express r in the equation as time, t, since it says dr/dt? If i want to find the radius at a specific time when the area increases as dA/dt = 0.03 (in)^2/sec would it the be correct to integrate dr/dt= 0.03/(2pi*r) to give me a function r which depends on t? If i want to express r as t in the eqation dr/dt= 1/(2pi*r)*0.03 , how exactly would i do it: I could isolate r in A=pi*r^2 --> sqrt(A/pi) and substitute sqrt(A/pi) into the equation and then to substitute t into A, i guess i would integrate dA/dt = 0.03 (in)^2/sec to get A=A(t)=0.03*t and then substitute A=0.03t like this dr/dt= 0.03/(2pi*(sqrt(0.03*t/pi) I don't know if I'm breaking any rules here? OR if my reasoning is wrong?