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Is this right? (Chain Rule - Calc I)

  1. Oct 17, 2012 #1
    Find the derivative of 101-x2.

    1.) So, I used power rule to get: (1-x2)(10-x2).
    2.) Then I did chain rule and multiplied my previous answer with (d/dx)(-x2).
    3.) The answer I get is: (-2x)(1-x2)(10-x2).


    When I use my calculator, the answer I get is: -20*ln(10)*10-x2. So, where does -20*ln(10) come from?
     
  2. jcsd
  3. Oct 17, 2012 #2
    The power rule applies when ##x## is the base, not in the exponent. What kinds of functions are the derivatives of the exponential function?
     
  4. Oct 17, 2012 #3
    You have to use the formula for a constant to a variable exponent..

    a^u = lna (u) (u')

    So you use properties of exponents to get 10 times 10 to the power of negative x squared..

    So that's a constant with a variable exponent..

    So you get 10(ln10)(10^-x^2)(-2x)
    ^u ^u'
    Then that simplifies to your answer, but you forgot the x.
     
  5. Oct 17, 2012 #4
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