PoofyPenguin
Could someone please help me? Attachments to come...
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PoofyPenguin
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Here is the question:
PoofyPenguin
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Here's what i got so far:
PoofyPenguin
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I'm not sure if i did it right and i'm not sure where it's going?
PoofyPenguin
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alright... i think i get it, but i don't get how or why the x becomes and e?
technopanda13
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fancy writing
PoofyPenguin
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@technopanda13 thank you!
zepdrix
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Haha I was thinking the same thing :D I love that multiply lil astrix XD
zepdrix
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Hmm your steps look really good. I don't see any mistakes. For your final answer I would rewrite the ugly exponential term back as x^(4x^4 + 2), The one in front.
zepdrix
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Oh need an explanation on the exponentiation + log thing?
baldymcgee6
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Yeah, it looks good to me too. But where did the e and the natural log all the sudden appear from?
PoofyPenguin
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it was part of the hint...but i'm not sure why it works that way...
baldymcgee6
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What does the question ask?
PoofyPenguin
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@baldymcgee6 have a look at the attachment! it's the one labeld problem 10
Fazeelayaz
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X^(x2+2) is same as e^(4x2+2)lnx u can use calculator to verify
PoofyPenguin
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@Fazeelayaz alright, but how would i go about simplifying it?
zepdrix
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|dw:1351311147700:dw|
baldymcgee6
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ohh. sorry, I only saw you're answer :/
PoofyPenguin
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@zepdrix i'm glad you like my astrix ;)
Fazeelayaz
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simplyfying the answer or u want to know how they r equal
PoofyPenguin
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@zepdrix great explanation! I understand it now! But how to simplify?
baldymcgee6
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@PoofyPenguin the reason they give you that hint is to avoid logarithmic differentiation. But for future derivatives, I would recommend learning log diffs.
This is just a loophole around it! But good work, it looks good to me.
zepdrix
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|dw:1351311341113:dw|
zepdrix
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Ah yes logarithmic differentiation is a good skill to have c:
zepdrix
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What you have written for f'(x) is perfect poof, you just want to rewrite the first part without the e and natural log, undo your FIRST step that you did to it.
Fazeelayaz
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o i understand there is another way to solve take ln on both sides of ur question the equation becomes
\[\ln f(x)=(4x{4}+2)lnx\]
Fazeelayaz
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now differentiate both sides by x
technopanda13
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__━━____┓━╭━━━━━╮
____━━____┗┓|::::::::::^━━^
____━━____━┗|:::::::: |｡◕‿‿◕｡|
____━━____━━╰O--O----O-O-╯ here is a cat for for all you hard workers
zepdrix
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hah :D
PoofyPenguin
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alright! so would this be the final answer or can it be simplified more?
Fazeelayaz
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\[1/f(x)*(df(x)/dx)=...\]use product rule on left side
PoofyPenguin
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@technopanda13 cute kitty! ;P
zepdrix
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You could get a common denominator on the inside if you wanted to, but it totally unnecessary c: Yah it looks good there.
Fazeelayaz
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yes u have done it that's right
PoofyPenguin
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ok! let me type it into the computer and get meh marks! :D
PoofyPenguin
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Yayayayayayayay! I got it! Thanks so much everyone! All of you were so helpful! :D
zepdrix
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yay team \:D/