# Homework Help: Derivatives Problem (Calculus I)

1. Nov 7, 2012

### PotentialE

1. The problem statement, all variables and given/known data
find d/dt for a rectangle.

2. Relevant equations
A=bh
product rule for derivatives (the first times the derivative of the second plus the second times the derivative of the first)
Chain rule for derivatives

3. The attempt at a solution
If b is a constant, then I know that dA/dh = b (this was the previous problem in which I could solve)
my issue with the current problem is that this variable t that I'm supposed to take the derivative with respect to is not in the problem- so how would I go about doing this?

My attempt:
d/dt (A=bh)
dA/dt = bh
dA/dt = (b(dA/dh)) + (h(dA/db))
My only problem with this solution is that I think there should be a d(b or h)/dt on the right side of the equation because of the chain rule

could someone please explain where/why the variable t comes in and what the correct answer is? Thank you!!

2. Nov 7, 2012

### micromass

I have no clue what this means. Can you quote the full problem as it appears in your book?

3. Nov 7, 2012

### PotentialE

that's my problem too... that IS the quote!

"Find d/dt for a rectangle" and then the formula given is A=bh
so find d/dt for A=bh

4. Nov 7, 2012

5. Nov 7, 2012

### PotentialE

On a previous problem:
Find d/dt for a square

d/dt (A=s2)

dA/dt = 2s (ds/dt)

perhaps you understand this one? (I don't)
well i know the derivative of s2 = 2s. so we've taken the derivative of A with respect to t... so perhaps multiplying 2s by ds/dt is part of the chain rule or something... I don't really know where ds/dt came from

6. Nov 7, 2012

### SammyS

Staff Emeritus
Assume that b and h are both functions of time.

There should be no derivatives of A on the right hand side of the following:

dA/dt = (b(dA/dh)) + (h(dA/db))

Use the product rule to find [itex]\displaystyle \frac{d}{dt}(b\,h)\ .[/itex