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can someone help me step by step?
find the derivative
y=ln((e^(7x))/(sqrt(4x5)))
 one year ago
 one year ago
can someone help me step by step? find the derivative y=ln((e^(7x))/(sqrt(4x5)))
 one year ago
 one year ago

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satellite73Best 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
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
it is the log of the whole thing right?
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
so first step would be, before beginning to take the derivative, rewrite as \[\ln(e^{7x})\frac{1}{2}\ln(4x5)\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
are those steps clear?
 one year ago

monroe17Best ResponseYou've already chosen the best response.1
why is 1/2 there and not (4x5)^(1/2)
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
i used two facts \[\log(\frac{a}{b})=\log(a)\log(b)\] and \[\log(a^n)=n\log(a)\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
because \[\log(\sqrt{4x5})=\log((4x5)^{\frac{1}{2}})=\frac{1}{2}\log(4x5)\]
 one year ago

monroe17Best ResponseYou've already chosen the best response.1
but 1/2 is outside the () and not inside ?
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
You can use the rule like that. As long as it's insside the log.
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
the one half comes right out front as a multiplier
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
on other words, \(\log(\sqrt{x})=\frac{1}{2}\log(x)\)
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
then one more step before differentiating since log and exp are inverse functions, you have \[\log(e^{7x})=7x\]
 one year ago

monroe17Best ResponseYou've already chosen the best response.1
okay, so do i need to use product rule for 1/2ln(4x5)?
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
\(\frac{1}{2}\) is just a constant , leave it there
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
Well you could... But it's a waste of time.
 one year ago

satellite73Best 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 \(\frac{3}{2}x^2\)
 one year ago

monroe17Best ResponseYou've already chosen the best response.1
gotcha. the power rule^
 one year ago

satellite73Best 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
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
typo there, i meant \[7x\frac{1}{2}\ln(4x5)\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
ok let me know what you get
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
It will be useful when you do the ln part.
 one year ago

sirm3dBest ResponseYou've already chosen the best response.0
oops, you forgot to differentiate 7x
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
careful of the first term derivative of \(7x\) is just \(7\)
 one year ago

satellite73Best 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
 one year ago

monroe17Best ResponseYou've already chosen the best response.1
i thought i was just doing chain rule? i know that that's 7?
 one year ago

satellite73Best 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
 one year ago

monroe17Best ResponseYou've already chosen the best response.1
i did the chain rule for ln(4x5) not 1/2*ln(4x5)
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
yea it is right what you wrote is correct
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
the "minus one half" is just a constant, leave it there like you did
 one year ago

monroe17Best ResponseYou've already chosen the best response.1
okay, so where do i go from there. that fraction you did confused me.
 one year ago

satellite73Best 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
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
you wrote this 7x1/2*(1/4x5)*4
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
the 7x should be 7
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
and the four is in the numerator, cancels with the 2 in the denominator
 one year ago

monroe17Best ResponseYou've already chosen the best response.1
derivative of 7x is 7. 1/2 of 4 is 2. 72/4x5
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
so it should look more like \(7\frac{2}{4x5}\)
 one year ago

monroe17Best ResponseYou've already chosen the best response.1
thanks! im just a little slow sometimes lol
 one year ago
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