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Write then nth derivative of log(axb) |
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Answer» First we need to do a change of BASE from 10 to e. log x = ln x / ln 10 = (1 / ln 10) ln x Then as you start taking derivatives, the (1 / ln 10) will just be a constant. The first derivative of ln x is 1/x The second derivative of ln x is -1/(x^2) The third derivative of ln x is 2 /(x^3) The fourth derivative of ln x is -6/(x^4) See the PATTERN? The derivatives alternate between positive and NEGATIVE. We will accomplish this with the standard (-1)^(n+1). The value of the coefficient is (n-1)! This is all times (1 / x^n). And do not forget the constant ( 1 / ln 10 ) So the nth derivative of log x is ( 1 / ln 10) ((-1)^(n+1)) (n-1)! (1 / x^n) Fun |
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