V(h) = pie/3(R^2h-h^3)

Question

take the derivative with respect to h.

using the chain rule I got:

V'(h) = pie/3(2Rh+R^2-3h^2)

but this is not the correct answer. what did I do wrong?

Answer 1

I would prefer to write the V equation as
V(h) = (pi/3)(R^2*h-h^3)
to emphasize that the (R^2h-h^3)
term is not in the denominator.

Unless R is a function of h, you do not have to use the chain rule. You have said nothing that implies that R is a function of h. R and h are independent variables. �ÝV/�Ýh is really a partial derivative.

Consider R as a constant when differentiating with respect to h.

V'(h) = (pi/3)R^2 - pi*h^2

Answer 2

Ignore �ÝV/�Ýh

Jiskha would not allow me to type the rounded-d symbol for d in the partial derivative.

Answer 3

thanks!