Question

math question from applications of the derivatives.

maths formula:

V = 4/3(pi)r^3

dV = 4(pi)(3r^2)
= 4(pi)r^2

But I don't understanding that how to get (3r^2) ?

Answer 1

d/dr (r^3) = 3r^2

It's just the normal power formula

So,

dV/dr = (4/3)pi (3r^2)

dV = 4pi r^2 dr

Don't lose track of the dr when doing related rates