Question

Given y/x = (arccos(x))ln x. Find dy/dxusing logarithmic differentiation

Answer 1

\[ y=xcos^{-1} (x)\ln(x)\]

Answer 2

?

Answer 3

They are usually not the sort of things you use logarithmic differentiation for. You only really use it when your variables are indicies.

Answer 4

what, I think I get it . You can split up the log.

Answer 5

\[\ln(y) = \ln(x \cos^{-1}(x)\ln(x))\]

Answer 6

\[\ln(y) = \ln(x) +\ln( \cos^{-1}(x)) + \ln(\ln(x))\]

Answer 7

\[\frac{1}{y} \frac{dy}{dx} = \frac{1}{x} - \frac{1}{\cos^{-1}(x)\sqrt{1-x^2} } + \frac{1}{xln(x)}\]

Answer 8

fairly sure that's it.

Answer 9

i was wondering myself why they asked for logarithmic differentiation

Answer 10

\[\frac{dy}{dx} = x \cos^{-1}(x)\ln(x) [ \frac{1}{x} - \frac{1}{\cos^{-1}(x) \sqrt{1-x^2}}+\frac{1}{xln(x)}]\]

Answer 11

thank you very much elecengineer