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Chain rule in Calc = Chain in Log?

  1. Jun 5, 2003 #1
    I know in Logarithms loga b * logc d = loga d * logc b

    and

    loga b * logb c = loga c.

    Chain Rule.

    Now I read Calculus, I found out about the Chain rule, are they the same?? Looks like it. But because of my poor English reading, I couldn't understand the text. Can some one explain what Chain rule is?
     
  2. jcsd
  3. Jun 5, 2003 #2
    They are not related. if you have several functions as arguments to other functions like f( g( h(x) ) ), then the derivative of this is f'( g( h( x ) ) ) * g'( h( x ) ) * h'( x ) do you see the pattern? So for f(x) = 1/x and g(x) = ln(x) and h(x) = x2, f( g( h (x ) ) ) = 1/ln(x2) and the derivative would be -1/(ln(x2)2) * 1/(x2)*2x
     
  4. Jun 9, 2003 #3

    Dx

    User Avatar

    great website

    chain rule
    Dx :wink:
     
  5. Jun 11, 2003 #4
    So what is the derivative of n^x, suppose n is a real number, and x is an unknown. And power rule does not apply to this situation because x is not a real number.
     
  6. Jun 11, 2003 #5
    let f(x) = nx
    ln f(x) = x ln n (take ln on both sides)
    f '(x)/f(x) = ln n (take the first derivative on both sides)
    f '(x) = f(x)*ln n = nxln n

    PS
    1) ln is natural log (base e), only natural log can be used in differentiation.

    2) d/dx ln f(x) = f '(x)/f(x)
     
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