Expert: Paul Klarreich - 10/1/2008

Question
Dear Paul, I'm taking calculus 1 and was hoping that you might be able to help with finding the instantaneous rate?

Find the instantaneous rate of change of w with respect to z for w = (1/z) + (z/2)

Answer
Questioner:   Sharon
Category:  Calculus
Private:  No
 
Subject:  Instantaneous rate of change
Question:  Dear Paul, I'm taking calculus 1 and was hoping that you might be able to help with finding the instantaneous rate?

Find the instantaneous rate of change of w with respect to z for w = (1/z) + (z/2)
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Hi, Sharon,

The phrase "instantaneous rate of change of w with respect to z"  is the same as dw/dz.  So you just differentiate:

w = z^-1 + z/2

dw/dz = -z^-2 + 1/2 = -1/z^2 + 1/2, etc.

That's all.  If you have a specific value of z, you substitute it.