anonymous
  • anonymous
Find dy/dx for y=ln(5−x)^6
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[y = \ln(5-x)^6\] take derivative : \[\frac{dy}{dx} = 6 \cdot \ln(5-x)^5 \frac{d(5-x)}{dx}\]
anonymous
  • anonymous
anonymous
  • anonymous
It is by chain rule.. In chain rule we are using power rule also which says : \[y = f(x)^n\] \[\frac{dy}{dx} = n \cdot f(x)^{n-1} \cdot \frac{d(f(x))}{dx}\]

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anonymous
  • anonymous
Wait, isn't that in the case that the 6th power would be to the entire thing? I thought you brought the 6 in front since lna^b=blna
anonymous
  • anonymous
\[\frac{dy}{dx} = 6 \cdot \ln(5-x)^5 \frac{d(\ln(5-x)}{dx} \cdot \frac{d(5-x)}{dx}\]
anonymous
  • anonymous
ln((x-5)^6) = 6ln(x-5) ( 6ln(x-5) ) ' = 6/(x-5)
anonymous
  • anonymous
Mixing up things...
anonymous
  • anonymous
oh! duh! Got it, thank you!!1
anonymous
  • anonymous
\[y = \ln(5-x)^6\] \[\frac{dy}{dx} = \frac{1}{(5-x)^6} \times 6 \times (5-x)^5 \times (-1)\]
anonymous
  • anonymous
Is this right???
anonymous
  • anonymous
It will reduce to : \[\frac{dy}{dx} = \frac{-1}{(5-x)}\]
anonymous
  • anonymous
ln((5-x)^6) = 6ln(5-x) ( 6ln(5-x) ) ' = -6/(5-x)
anonymous
  • anonymous
Forgot 6 there.. Oh God...
anonymous
  • anonymous
\[\frac{dy}{dx} = \frac{-6}{(5-x)}\]
anonymous
  • anonymous
Yes by power rule, you can bring 6 in front: \[y = 6 \cdot \ln(5-x)\] Now take the derivative..
anonymous
  • anonymous
Okay, I've got it figured out! Thank you! If you'd like to help some more I just posted another question :)

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