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monroe17
Group Title
can someone help me step by step?
find the derivative
y=ln((e^(7x))/(sqrt(4x5)))
 2 years ago
 2 years ago
monroe17 Group Title
can someone help me step by step? find the derivative y=ln((e^(7x))/(sqrt(4x5)))
 2 years ago
 2 years ago

This Question is Closed

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
before you begin taking the derivative, use the properties of the log to make this expression easier to differentiate
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
it is the log of the whole thing right?
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
so first step would be, before beginning to take the derivative, rewrite as \[\ln(e^{7x})\frac{1}{2}\ln(4x5)\]
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
are those steps clear?
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
why is 1/2 there and not (4x5)^(1/2)
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
i used two facts \[\log(\frac{a}{b})=\log(a)\log(b)\] and \[\log(a^n)=n\log(a)\]
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
because \[\log(\sqrt{4x5})=\log((4x5)^{\frac{1}{2}})=\frac{1}{2}\log(4x5)\]
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
but 1/2 is outside the () and not inside ?
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
You can use the rule like that. As long as it's insside the log.
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
the one half comes right out front as a multiplier
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
on other words, \(\log(\sqrt{x})=\frac{1}{2}\log(x)\)
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
then one more step before differentiating since log and exp are inverse functions, you have \[\log(e^{7x})=7x\]
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
okay, so do i need to use product rule for 1/2ln(4x5)?
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
oh no not at all
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
\(\frac{1}{2}\) is just a constant , leave it there
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Well you could... But it's a waste of time.
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
for example if you wanted the derivative of \(\frac{1}{2}x^3\) you do not use the product rule, you just say \(\frac{3}{2}x^2\)
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
gotcha. the power rule^
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
so now you have \[7x+\frac{1}{2}\ln(4x5)\] so the only rule you need now is the chain rule for the second part, and also knowing what the derivative of the log is
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
typo there, i meant \[7x\frac{1}{2}\ln(4x5)\]
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
okay imma try it/
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
ok let me know what you get
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
dw:1351998238123:dw
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
It will be useful when you do the ln part.
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
(1/4x5)*4?
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
7x1/2*(1/4x5)*4
 2 years ago

sirm3d Group TitleBest ResponseYou've already chosen the best response.0
oops, you forgot to differentiate 7x
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
careful of the first term derivative of \(7x\) is just \(7\)
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
and you might not want to write \[\frac{4}{2(4x5)}\] since you can cancel a 2
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
i thought i was just doing chain rule? i know that that's 7?
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
chain rule for \(\frac{1}{2}\ln(4x5)\) because it is a composition , the log of something for \(7x\) that is just a line with slope 7, derivative is 7
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
woah im lost now.
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
i did the chain rule for ln(4x5) not 1/2*ln(4x5)
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
yea it is right what you wrote is correct
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
the "minus one half" is just a constant, leave it there like you did
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
okay, so where do i go from there. that fraction you did confused me.
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
the only mistake in your answer was that you left \(7x\) there, when the derivative of \(7x\) is \(7\) everything else was right
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
you wrote this 7x1/2*(1/4x5)*4
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
oh i get it now!
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
the 7x should be 7
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
and the four is in the numerator, cancels with the 2 in the denominator
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
derivative of 7x is 7. 1/2 of 4 is 2. 72/4x5
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
so it should look more like \(7\frac{2}{4x5}\)
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
yup you got it
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
thanks! im just a little slow sometimes lol
 2 years ago
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