<p>thank you, i forget that x is not a constant power,but which formula should i use?</p>
<p>gosh,i didn’t notice there are threee posts above me,thank you!:)))</p>
<p>It’s all algebra up to ln y = x ln x.</p>
<p>d/dx(ln y) = (1/y)(y’)
d/dx(xlnx) = (x)(1/x) + (ln x)(1) = (x/x) + (ln x) = 1 + ln x</p>
<p>(1/y)(y’) = (1 + ln x)
Divide both sides by 1/y.
y’ = (1 + ln x) / (1/y)
Simplify.
y’ = y(1 + ln x) = y + yln x</p>
<p>Since y = x^x…</p>
<p>y’ = x^x(1 + ln x) = x^x + (x^x)ln x</p>
<p>^thanks:)
So now my question is:Under what circumstances do we need to ln both sides?</p>
<p>You ln both sides to bring down the x in x^x.</p>
<p>Does that mean we need to ln both sides when the power is not a constant number?
Thank you!</p>
<p>i would be appreciated to any response to my question.</p>
<p>I can answer my question now.:)</p>
<p>[url=<a href=“http://www.wolframalpha.com%5DWolfram%7CAlpha%5B/url”>http://www.wolframalpha.com]Wolfram|Alpha[/url</a>]
Best site in the world.</p>
<p>^Wow… what an amazing site.</p>
<p>The derivative should be -3 sin 3x.</p>
<p>Woops I didn’t read the cube part. lol</p>
<p>that site is so cool=)</p>
<p>thanks for offering:)</p>
<p>i just found a mistake on the site:[5th</a> largest country - Wolfram|Alpha](<a href=“5th largest country]5th - Wolfram|Alpha”>5th largest country - Wolfram|Alpha)</p>
<p>when you scroll down,you will see the population isn’t true,china should be 13.1 billion,india should be 11.7 billion,but shrink 10 times on the stats they offer</p>
<p>So we can’t believe al lof them.</p>
<p>Haha maybe not. Nevertheless that site helped me limp through AB Calculus so I would remember it if I were you :)</p>
<p>i just can’t find a verbal expalanation, how to solve y=tan e^x?
Thank you for writting down the procedure.:)</p>
<p>this would be my last question on this thread…</p>