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derivative of (ln(x))^x

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Thread replies: 10
Thread images: 2

Anonymous
derivative of (ln(x))^x 2016-11-14 03:03:49 Post No.
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derivative of (ln(x))^x Anonymous 2016-11-14 03:03:49 Post No. [Report]
can someone do this and show explicit work?
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Anonymous 2016-11-14 05:43:13 Post No.220302
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Anonymous 2016-11-14 05:43:13 Post No.220302 [Report]
all my smartest friends can't figure this out... so bamp
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Anonymous 2016-11-14 06:11:43 Post No.220308
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Anonymous 2016-11-14 06:11:43 Post No.220308 [Report]
>>220248
ask /sci/
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Anonymous 2016-11-14 07:12:15 Post No.220326
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Anonymous 2016-11-14 07:12:15 Post No.220326 [Report]
try formal defination of derivatives
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Anonymous 2016-11-14 07:21:08 Post No.220330
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Anonymous 2016-11-14 07:21:08 Post No.220330 [Report]
lnx)^x*ln(lnx)*1/x
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Anonymous 2016-11-14 07:32:31 Post No.220335
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Anonymous 2016-11-14 07:32:31 Post No.220335 [Report]
File: calc3.png (16KB, 610x402px) Image search: [Google]
calc3.png
16KB, 610x402px
>>220248
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Anonymous 2016-11-14 09:09:05 Post No.220352
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Anonymous 2016-11-14 09:09:05 Post No.220352 [Report]
>>220335
Shouldn't second line be,

(ln)(y)=[(ln)(ln(x))]
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Anonymous 2016-11-14 10:32:31 Post No.220378
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Anonymous 2016-11-14 10:32:31 Post No.220378 [Report]
>>220352
Your notation of putting parenthesis around the ln and the thing it's acting upon is confusing, but I think this might explain that step.
I skipped one step inbetween:
lny = ln((lnx)^x)
lny = xln(lnx)
I just took the natural log of both sides. Using the rules of logarithms, I brought the x exponent to the front.
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Anonymous 2016-11-14 10:51:43 Post No.220380
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Anonymous 2016-11-14 10:51:43 Post No.220380 [Report]
>>220335
This is right OP.See this.
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Anonymous 2016-11-14 21:17:58 Post No.220664
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Anonymous 2016-11-14 21:17:58 Post No.220664 [Report]
>>220335
thanks anon i have a calc 1 midterm today
Thread posts: 10
Thread images: 2
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