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Use logarithmic differentiation to find the derivative of the functiony=(lnx)^(cos12x)...

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rachelgree | Student, College Freshman | (Level 1) eNoter

Posted March 8, 2012 at 10:38 AM via web

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Use logarithmic differentiation to find the derivative of the function

y=(lnx)^(cos12x)   ln of x to the power of cos12x

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted March 8, 2012 at 11:13 AM (Answer #1)

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`y= ln x^(cos12x) `

`==gt y= (cos12x)(lnx)`

Now we will use the product rule to find the derivative.

`==gt y' = (cos12x)'(lnx) + (cos12x)(lnx)' `

`==gt y'= (-12sinx)(lnx) + (cos12x)(1/x) `

`==gt y'= -12(sinx)lnx + (cos12x)/x`

 

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