Balwinder S.
asked • 06/07/22My question is on differentiation
Can anyone differentiate this without logarithmic differentiation?
(log x)cos x
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2 Answers By Expert Tutors
Doug C. answered • 06/07/22
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Doug C.
Here is a solution where log(x) is interpreted as common log. desmos.com/calculator/7nrcsbidvm
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06/07/22
Raymond B. answered • 06/07/22
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derivative of (lnx)^cosx = [(lnx)^cosx](cosx/ln(lnx) - sinxlnx(lnx)]
if you were taking a beginning course with an introduction to logs, then "log" woud be the common log with base 10. but this problem is suffiently advanced mathematics that "log" would have to mean the natural log with base e, "ln"
derivative of lnx^cosx
= (lnx^cosx)((cosx)'ln(lnx) + cosx(ln(lnx)')
= lnx^cos(1-sinx)(ln(lnx0 + cosx/lnx)(lnx)')
= lnx^cosx(cox/x/ln - xinln(lnx)
= lnx^cos(cosxlnx - sinln(lnx)
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Luke J.
Is that log base 10 of x or natural log of x? changes the procedure a bit if it's base 10 and not natural log.06/07/22