anonymous
  • anonymous
how would i find the derivative of tanx-3cos5x?
Mathematics
schrodinger
  • schrodinger
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jessica
  • jessica
do it in parts. First deal with tanx
anonymous
  • anonymous
so (sinx/cosx) ?
jessica
  • jessica
the derivative of tan is \[\sec ^{2}x\]

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jessica
  • jessica
sure you could also do it that way
anonymous
  • anonymous
i know, but my teacher wants us using cos and sin identities right now
jessica
  • jessica
then use the quotient rule
jessica
  • jessica
have you learned the quotient rule?
anonymous
  • anonymous
yes, but using it with these kinds of problems is still not second nature, you know?
jessica
  • jessica
ya it will come with practice it's bottom times the derivitave of the top plus top times the derivative of the bottom all over the bottom squared.
anonymous
  • anonymous
so i consider the top to be (sinx/cosx) and the bottom to be...?
jessica
  • jessica
so cosx(cosx)-sinx(sinx)/\[\cos ^{2}x\]
anonymous
  • anonymous
cos squared x?
jessica
  • jessica
you will consider the top to be sinx and the bottom to be cos x
anonymous
  • anonymous
so in using the quotient rule, i only deal with tanx?
jessica
  • jessica
right that part goes on bottom and the other part goes on top so cos squared minus sin squared on top
jessica
  • jessica
in using the quotient rule you deal with sinx/cosx
anonymous
  • anonymous
In any problem where you derive a function, you derive each term seperately. That's why you use the quotient rule on the sin(x)/cos(x) only. You'll just add the result of that to the derivative of 3cos(5x). Do you know the derivative of sin(x) and cos(x)?
anonymous
  • anonymous
you need to use the chain rule...See the linky... http://www.wolframalpha.com/input/?i=derivative+of+tanx-3cos5x
anonymous
  • anonymous
and make sure you click on "Show the Steps"

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