Relevant equations the derivative equation

  • Thread starter Thread starter myria36
  • Start date Start date
  • Tags Tags
    Derivative
Click For Summary
SUMMARY

The discussion centers on calculating the derivative of the surface area of a right circular cylinder, represented by the formula A = 2πr(r + h), with respect to height (h) while keeping the radius (r) constant. The user, myria36, seeks guidance on differentiating the equation due to the presence of h in only one term. The derivative is ultimately expressed as dA/dh = (-2πr²h⁻²) + 2πr, indicating the rate of change of surface area concerning height.

PREREQUISITES
  • Understanding of calculus, specifically differentiation techniques.
  • Familiarity with the formula for the surface area of a right circular cylinder.
  • Knowledge of constant functions and their derivatives.
  • Ability to manipulate algebraic expressions involving variables and constants.
NEXT STEPS
  • Study the rules of differentiation, particularly the product and chain rules.
  • Learn how to apply implicit differentiation in cases where variables are interdependent.
  • Explore the concept of related rates in calculus for real-world applications.
  • Practice deriving equations involving multiple variables to strengthen understanding.
USEFUL FOR

Students studying calculus, educators teaching derivative concepts, and anyone looking to enhance their understanding of differentiation in geometric contexts.

myria36
Messages
2
Reaction score
0
#1
myria36

myria36 is Online:
Posts: 1
calculus - derivatives
1. Homework Statement

the total surface area of a right circular cylinder is given by the formula: (A = 2Pir(r + h) ).
where r is the radius and h is the height.
sub part a) find the rate of change of A with respect to h is r remains constant

**i know how to take derivatives. the only thing is that in this case, I am not sure how to take the derivative of h since it is only present in one term.

2. Homework Equations
the derivative equation
dA / dr


3. The Attempt at a Solution
i first distributed the 2pir, to yield
2pir^2 + 2pirh
2pir^2(h/h) + 2pirh -- i added the (h/h), which is like multiplying by 1, to add h to the first term- I am not sure if this is correct, but i was just guessing.

h (2pir^2 h^-1 + 2pi r)
now i am stuck here. i can't take the derivative of all the h's in my problem, because one h is still present in the equation.
**below is my attempt to still work with it.
dA/dh = 1 times [-1(2pir^2h^-2) + 2pir
final answer: (-2pir^2h^-2) + 2pir
please can someone guide me on the technique i should use for getting the area to be in terms of h. any and all replies are welcome and appreciated
 
Physics news on Phys.org


Hint: What's the derivative of a constant function?
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
4K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 6 ·
Replies
6
Views
11K
Replies
11
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 5 ·
Replies
5
Views
5K
  • · Replies 9 ·
Replies
9
Views
8K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K