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find dy/dx...if y=e^log[log(logx)]*log3X pls note log3x does not include in the exponent...help me pls...thanks in advance...


find dy/dx...if y=e^log[log(logx)]*log3X


pls note log3x does not include in the exponent...help me pls...thanks in advance...


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1 Answers

nikhil arora
54 Points
9 years ago

i have assumed that base of log is e (since u have not given)

using property elogx=x and writing elog[log(logx)]=log(logx) in the given problem.

 

y=log(logx)*log3x

 

now applying product rule and differentiating :

dy/dx= [d/dx(log{logx})] log3x + log(logx) [d/dx(log3x)]

dy/dx= (1/logx) d/dx(logx) log3x + log(logx) (1/3x) d/dx(3x)

dy/dx= log3x/xlogx + log(logx)/x

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