V(h) = pie/3(R^2h-h^3)
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?
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
Ignore �ÝV/�Ýh
Jiskha would not allow me to type the rounded-d symbol for d in the partial derivative.
thanks!
To find the derivative of V(h), which is the volume of a cone with respect to h, you correctly used the chain rule in differentiating the formula. However, it seems like you made a small mistake in differentiating the terms.
Let's by step by step look at the process:
Given function: V(h) = π/3(R^2h - h^3)
To find the derivative, you need to differentiate each term individually using the power rule, which states that the derivative of x^n is equal to n*x^(n-1).
1. Differentiate the first term: R^2h
- The derivative of R^2h with respect to h is 2R^2.
2. Differentiate the second term: -h^3
- The derivative of -h^3 with respect to h is -3h^2.
Now, combining the derivatives of the two terms, we have:
V'(h) = 2πR^2 - 3πh^2
So, the correct derivative of V(h) with respect to h is V'(h) = 2πR^2 - 3πh^2.