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...

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

using property e^logx=x and writing e^{log[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