Diffrentiation, Mathematics

y=f(a^x)   and f(sinx)=lnx find dy/dx?

Solution) dy/dx exist only when 01 as the function y = f(a^x) itself does not exist.

Posted Date: 3/8/2013 8:22:45 AM | Location : United States

dy/dx = (a^x)(lnx)f''''(a^x), .........(1)

but f(sinx) = lnx implies f(x) = ln(arcsinx)

hence f''''(x) = (1/arcsinx) (1/ ( ( 1-x^2 ) ^ ( !/2 ) ) implies f''''(a^x) = (1/arcsin(a^x)) (1/ ((1-a ^ (2x)) ^ (1/2))) ............(2)

hence from ...(1) &.....(2) the solution is obtained but it should br noted that the given solution exist only when x belongs to (0,1].

Posted by | Posted Date: 3/8/2013 8:23:08 AM

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