Expert: Paul Klarreich - 2/13/2008

Question
given the function f(x) = 10x + 3/x  evaluate the derivative of f(x) at x = 3  
How do I start this with a fraction 3/x ?   Am tyring to use d/dx(c)=0  
Thank you

Answer
Questioner:   Jill
Category:  Calculus
Private:  No
 
Subject:  Calculus: Differentiations
Question:  given the function f(x) = 10x + 3/x  evaluate the derivative of f(x) at x = 3  
How do I start this with a fraction 3/x ?   Am tyring to use d/dx(c)=0  
Thank you
.........................................
Hi, Jill,

Try  3/x = 3x^(-1), and use the x^n rule:  D(x^n) = n x^(n-1)

Remembering that subtracting 1 from something makes it smaller will avoid terrible mistakes here.

D(3/x) = D(3x^(-1)) = 3(-1)x^(-2) = -3/x^2

Also remember that the rule  D(c) = 0  says, in words: The derivative of a constant TERM is zero.  [Leave out that word 'term' and you will surely mess something up.]

The rest should be easy.