gistfile1.txt

The radius of a sphere is increasing at a rate of 7.5 meters per minute.
At a certain instant, the radius is 5 meters.
What is the rate of change of the surface area of the sphere at that instant (in square meters per minute)?

S (t) = 4* pi * [r(t)]^2 * ( dr/dt r(t))

Solve for derivative of S, the answer is 300 pi, just wondering how to model this in Octave. Im familiar with how to do one unknown and the symbolic package, just not sure how to do this one

Where the Surface of a sphere is 4 * pi * r^2

Hello @qorrect!
I'll try to help. I don't know if it is exactly what you want, but you could do this in Matlab (I'm using a R2016b version, so it could be different in other versions):

syms t
radius_rate = 7.5;
radius = radius_rate*t;
surf_area = 4*pi*radius^2;
surf_area_rate = diff(surf_area,t);
radius_goal = 5;
t_goal = solve(radius == radius_goal, t);
result = subs(surf_area_rate, t, t_goal);

... or more compact:

syms t
result = subs(diff(4*pi*(7.5*t)^2, t), t, solve(7.5*t==5,t));

Hope it helps!

Thank you @rballet it did help!