<p>Okay so I am finding the derivative of this function:
(3x-5)^4(4x+11)^5</p>
<p>I have so far gotten this far:
(3x-5)^4 (80x+220)^4 + (4x+11)^5 (36x-60)^3</p>
<p>How do I multiply them out? And if you're bored, am I doing this right so far?</p>
<p>i'm too lazy to do it, but shouldn't it be 12(3x-5)^3(4x+11)^5 + 20(3x-5)^4(4x+11)^4? i'm not sure where you got the 36, cuz you can't just distribute the deriv of the inner function to the corresponding polynomial... it would be a coefficient out front</p>
<p>Yeah I just realized that...but I still need to know what I do after that...:p</p>
<p>You've made a mistake with the derived terms. d/dx[(4x + 11)^5] = 20<em>(4x + 11)^4, not (80x+220)^4, and likewise d/dx[(3x - 5)^4] = 12</em>(3x - 5)^3.
Then just use algebra to simplify. You can first factor out a (4x + 11)^4, then a (3x - 5)^3.
I might be wrong here, but when I worked this out I got
3<em>(4x + 11)^4</em>(3x - 5)^3*(32x + 7).</p>
<p>i wouldn't simplify, collegeboard doesn't expect it why should you're teacher haha</p>
<p>I guess I should accept the fact I'm just going to fail calculus <em>sigh</em> Who cares that i've only passed one test this year</p>
<p>Because collegeboard math and calculus math are held at two completely different standards.</p>
<p>Arg, I posted too slow. This is in response to cujoe169's post.</p>
<p>
[quote]
i wouldn't simplify, collegeboard doesn't expect it why should you're teacher haha
[/quote]
It's neater, and comes in useful if you need to use that answer for something else, like if it was part of a physics problem.</p>
<p>I don't understand how I multiply it out though...argh. I don't know how to multiply out polynomials! :eek:</p>
<p>I see why I was wrong, but I'm still stuck with stupid polynomials.! :eek:</p>
<p>Just do it in baby steps, take as many lines as you need to. Look at what you get after using the product and chain rules, and try and find something to factor out. Then look and what you've got left, and try to factor out something else.</p>
<p>i'm too lazy to do it but use chain rule and product rule and the answer will come out in a jiffy.</p>
<p>i really see no point in simplifying this one once you get the derivative.. unless your teacher wants you to. If you have to simplify i think you start factoring out stuff but i really cant see where its gonna go</p>
<p>Yeah I'm factoring now. The calc teachers at my school are pretty much nazis when it comes to simplifying everything. I don't expect to pass this test (I still have to finnish this one AND do a 2nd derivative)</p>
<p>you do realize on the ap exam it's bad to simplify? mistakes happen... lol that sounds like a threat</p>
<p>Hm... if you absolutely want to simplify, just take it one step at a time.</p>
<p>For example:
(3x-5)^4</p>
<p>First, do (3x-5)(3x-5).
Then multiply the result of that by itself (or multiply it by (3x-5), and then multiply THAT result by (3x-5)).</p>
<p>Do this for every term, then multiply and add the simplified versions.</p>
<p>Implicit differentiation with ln</p>
<p>y = (3x-5)^4(4x+11)^5
ln y = ln ((3x-5)^4(4x+11)^5) = 4 ln (3x-5) + 5 ln (4x+11)</p>
<p>Easy from there.</p>