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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1so 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

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

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

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

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

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

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

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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1chain 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

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

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

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

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

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

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

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

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

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

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