anonymous
  • anonymous
find the derivative of y=log10(5x^4-2/x^3)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
this involves both the chain rule and the quotient rule
Mimi_x3
  • Mimi_x3
or you can use log laws to change it first; then diferentiate it, would be easier.
anonymous
  • anonymous
@failmathmajor only the 2/x^3 is a fraction

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Mimi_x3
  • Mimi_x3
is it \[\log\left(5x^{4}-\frac{2}{x^{3}}\right) ?\]
anonymous
  • anonymous
that would be much easier
anonymous
  • anonymous
so using log properties you can say that \[\log_{10} {x} = \ln x / \ln 10 \]
anonymous
  • anonymous
ln10 is a constant, you can factor that out
anonymous
  • anonymous
can you use the chain rule fluently?
anonymous
  • anonymous
y'=pu(x) * u'(x) right?
anonymous
  • anonymous
d(f(g(x))/dx = (dg(x)/dx)*(df(g(x))/dx) is the way I know it
Mimi_x3
  • Mimi_x3
Or..\[y= \log\left(5x^{4}-\frac{2}{x^{3}}\right) y = \log\left(\frac{5x^{7}-2}{x^{3}}\right) => y = \log\left(5x^{7}-2\right) - \log(x^3)\] Might be easier; than the quotient role and chain rule..
anonymous
  • anonymous
that may look confusing now that I see it
anonymous
  • anonymous
don't need the quotient in this case: can treat /x^3 as a x^-3
Mimi_x3
  • Mimi_x3
@cunninnc: are you able to do it now?
anonymous
  • anonymous
and you would still need the chain rule for that anyway
anonymous
  • anonymous
but enough arguing
Mimi_x3
  • Mimi_x3
Did an argument started? lol
anonymous
  • anonymous
\[(d(\ln (5x^4 - 2x^{-3}))/dx )/ \ln10\] is what it simplifies down to, to be concise
anonymous
  • anonymous
@Mimi_x3 kinda .... i see mr. moose got 2x^-3 where does ^-3 come froms
anonymous
  • anonymous
\[2/x^3= 2 * x^{-3}\]
Mimi_x3
  • Mimi_x3
Sorry i don't know what MrMoose is doing. @MrMoose: Use \frac{x}{y} for fractions :)
Mimi_x3
  • Mimi_x3
Or why not try the method that i used :) \[ \frac{d}{dx} \log\left(5x^{7}-2\right) -\frac{d}{dx} \log(x^3)\]
anonymous
  • anonymous
when you divide you subtract exponents, so that is equivalent to saying \[2 * \frac{x^0}{x^3}\] then subtract exponents in division
anonymous
  • anonymous
\[\frac{\frac{d(\ln(5x^4−2x^{−3}))}{dx}}{\ln10}\]
anonymous
  • anonymous
@catamountz15 what?
anonymous
  • anonymous
I am almost entirely sure that that isn't a form of the answer.
anonymous
  • anonymous
Here are the steps in to solving this problem.
anonymous
  • anonymous
that isn't what you wrote though
anonymous
  • anonymous
My apologies that was an answer to a different problem.

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