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

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0before you begin taking the derivative, use the properties of the log to make this expression easier to differentiate

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0it is the log of the whole thing right?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so first step would be, before beginning to take the derivative, rewrite as \[\ln(e^{7x})\frac{1}{2}\ln(4x5)\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0are those steps clear?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0why is 1/2 there and not (4x5)^(1/2)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i used two facts \[\log(\frac{a}{b})=\log(a)\log(b)\] and \[\log(a^n)=n\log(a)\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0because \[\log(\sqrt{4x5})=\log((4x5)^{\frac{1}{2}})=\frac{1}{2}\log(4x5)\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0but 1/2 is outside the () and not inside ?

anonymous
 3 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.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0the one half comes right out front as a multiplier

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0on other words, \(\log(\sqrt{x})=\frac{1}{2}\log(x)\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0then one more step before differentiating since log and exp are inverse functions, you have \[\log(e^{7x})=7x\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0okay, so do i need to use product rule for 1/2ln(4x5)?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\(\frac{1}{2}\) is just a constant , leave it there

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0for example if you wanted the derivative of \(\frac{1}{2}x^3\) you do not use the product rule, you just say \(\frac{3}{2}x^2\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0gotcha. the power rule^

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0typo there, i meant \[7x\frac{1}{2}\ln(4x5)\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0ok let me know what you get

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1351998238123:dw

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

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0careful of the first term derivative of \(7x\) is just \(7\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0and you might not want to write \[\frac{4}{2(4x5)}\] since you can cancel a 2

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i thought i was just doing chain rule? i know that that's 7?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0chain 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i did the chain rule for ln(4x5) not 1/2*ln(4x5)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yea it is right what you wrote is correct

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0the "minus one half" is just a constant, leave it there like you did

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0okay, so where do i go from there. that fraction you did confused me.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0the only mistake in your answer was that you left \(7x\) there, when the derivative of \(7x\) is \(7\) everything else was right

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0you wrote this 7x1/2*(1/4x5)*4

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0and the four is in the numerator, cancels with the 2 in the denominator

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0derivative of 7x is 7. 1/2 of 4 is 2. 72/4x5

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so it should look more like \(7\frac{2}{4x5}\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0thanks! im just a little slow sometimes lol
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