anonymous
  • anonymous
Cal 1: Find the derivative of:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
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Luigi0210
  • Luigi0210
you could use the quotient rule?
anonymous
  • anonymous
I understand I need to use the quotient rule, but i am still stuck. I would like an explanation of the steps if possible.

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Psymon
  • Psymon
Both are powers of 8, right?
anonymous
  • anonymous
Yes they are
Psymon
  • Psymon
Alright, well, no need for quotient rule to be honest. Start off by splitting it into two fractions.
Luigi0210
  • Luigi0210
Well you could use the quotient rue or do it by @Psymon 's way..
anonymous
  • anonymous
My answer so far is, (x)(e^8-8x^7)-(e^8-x^8)(1) / (x)^2 I havent learned Psymons rule before. We are learning the quotient rule.
Psymon
  • Psymon
This isn't really a rule. Do you know how to make this into 2 fractions?
Luigi0210
  • Luigi0210
btw, e^x=e^x and e^k=0
Luigi0210
  • Luigi0210
Right @Psymon
anonymous
  • anonymous
Oh woops. I forgot about the e^k=0 rule. That should make it much easier.
Luigi0210
  • Luigi0210
Yup :)
Psymon
  • Psymon
Yeah, its just a constant.
Psymon
  • Psymon
I just thought this would be simpler: \[\frac{ e ^{8} }{ x }-x ^{7} \]
anonymous
  • anonymous
one of those trick questions like find the derivative of \(f(x)=x^2+\sqrt{2}\)
anonymous
  • anonymous
Ok I see what you did there Psymon.
Luigi0210
  • Luigi0210
You can always count on Psymon to have it his way
Psymon
  • Psymon
Find derivative of: \[\log_{\cos^{-1}5 }(\sin ^{\frac{ \sqrt[16]{\pi} }{ \cos(e)}}) \]= 0 haha Yah, one of those trick things like satelite said. And yeah, x^7 is easy to differentiate. Really, e^8/x is easy, too. Mind if I show ya a trick for thos simple fraction derivatives?
anonymous
  • anonymous
Yes please. I will take any advice!
Psymon
  • Psymon
Alright, so given you have a fraction you need to take the derivative of. Something simple like: \[\frac{ 8 }{ x ^{3} } \] 3 steps: 1. Change the sign. 2. Multiple thepower of x into the numerator 3. Raise the power of x by 1. Doing that gives us a quick -24/x^4. Derivative of that = 96/x^5, derivative of thatis -480/x^6. I get thosenear instantly by following that 3 step pattern.
anonymous
  • anonymous
Ok i think i understand. It's kinda the same thing as bringing the entire denominator up and changing the sign of the exponent?
Psymon
  • Psymon
Right. Except instead of actually doing that, you recognize the pattern and just follow the steps. If you know theres a pattern then no need to do the process every single time.
anonymous
  • anonymous
OK i gotcha. Well that will help out a ton. Thanks :)
Psymon
  • Psymon
Yeah, np ^_^
Psymon
  • Psymon
so we got -e^8/x^2 - 7x^6, right? xD
anonymous
  • anonymous
Yup! Thanks!
Psymon
  • Psymon
Good job xD

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