I'm too lazy to check your solution, but you can get another faster one by setting
Can anyone help me figure out what I'm doing wrong:
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I've done it several times and gotten the same answer, unfortunately it's an even problem so I can't check my book, but Function calculator says the answer should be:
Wow, that was so elegant! (I was so focused on using the method just taught to us that I didn't even consider alternatives)
I used your method, and it came out the same as mine, I'll assume the function calculator's answer was the same as mine, and when I checked it that I checked it incorrectly. (if not that, then I did your way wrong in the same manner I did my way wrong, and if not that, then the function calculator is wrong, and if not that, then math is broken)
It's not elegant, it's just a faster way to avoid boring trig. calculations and the square root.
I suggest when you want to verify if your answer is correct or not, see solving derivatives step-by-step. If your result does not match with the software, then you're messing with some calculation. (Of course, software may fail.)
Math can't be broken
Oh wow! That would have saved me hours and hours last semester. I remember when I was first learning derivatives, and I got confused about the power rule, and hadn't found all the resources that I have now. And I spent this weekend doing the same problems over and over and over, like each problem 40 times, and comparing my answers from each time to see which ones I came up with the most to decide which ones I thought were most likely to be correct.
Maybe "broken" isn't an appropriate term, just expressing the idea of an unknown variable which causes math to be different than we understand it to be. (Note that I understand the unlikelihood of this possibility, which is why I placed it at the end of the list of possibilities.)
Thank you, I've been doing these problems all day each day all week, my head is swimming, so nice to have objective verification.
I'll just put my 2 cents worth in here (1 cent for each point):
1. Colby, you dropped a minus - it's in the edit and needs to be carried through to the end.
2. The answer of can be simplified by taking out a common factor of :
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Some obvious variant of this final answer is what a CAS is likely to spit out. And indeed what I'd expect to see as the correct option if it was a multiple choice question ..... And indeed, the answer in the back of the book (if the book gave answers to even numbered questions as well)