anonymous
  • anonymous
Let f(x)=cos(lnx). Then f′(x):
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
chain rule for this one \[f(g(x))'=f'(g(x))\times g'(x)\]
anonymous
  • anonymous
use \[f(x)=\cos(x), g(x)=\ln(x)\] so you have \[f(g(x))\]
anonymous
  • anonymous
you got this?

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anonymous
  • anonymous
i can write the answer if you like
anonymous
  • anonymous
Let me try to work it out, and see what I get first just so I can know if I am understanding it. Is that okay?
anonymous
  • anonymous
yes of course that is best
anonymous
  • anonymous
I tried and I got confused along the way. Can you tell me the answer now? I want to see how close I was.
anonymous
  • anonymous
ok in english "derivative of the outside function evaluated at the inside function, times the derivative of the inside function" you have \[\cos(\ln(x))\] derivative of cosine is - sine so start with \[-\sin(\ln(x))\] then multiply by the derivative of \(\ln(x)\) which is \(\frac{1}{x}\) to get \[-\sin(\ln(x))\times \frac{1}{x}=-\frac{\sin(\ln())}{x}\]\]
anonymous
  • anonymous
I was pretty close, just not close enough! Thanks!!

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