Kenneth S. answered • 06/10/18
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Expert Help in Algebra/Trig/(Pre)calculus to Guarantee Success in 2018
This differentiation requires application of several rules, including
a) derivative of a log is the reciprocal of the argument
b) derivative of a quotient has its own rule
c) the power rule, even when the exponent is a fraction
d) the chain rule is applicable to derivatives involving composition.
Also, care must be taken when the word "log" is used, whether one can assume that common logarithm is intended.
I notice a strange dot(.) appearing immediately after the caret that indicates exponentiation. Because of the above two dubious aspects of this function, I am not going to jump in and do possibly wasted typing.
Philip P.
tutor
We know that d ln(x)/dx = 1/x. However, for a different base log, you must convert it to base e (ln) before taking the derivative:
loga(x) = ln(x)/ln(a) so d(loga(x))/dx = (1/ln(a)) dln(x)/dx = 1/(ln(a)·x)
For your problem, a = 10 and your solution is correct except you are missing a 1/ln(10) for each term.
1/ln(10) + 3/[4 ln(10) (x-2)] - 1/[ln(10) (x+2)]
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06/10/18
Pragyan M.
06/10/18