IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

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can u differentiate log(log(|sin x|)) for all values of x.justify your answer?

shobhita

ans::cosx/log|sinx| |sinx|

this ans is invalid for x=90 and x=0;
for x=90 =>log sinx=0
and for x=0=>
sinx=0;
rate please

johri_anshuman

first find the domain of the given function

f(x)=log{log(|sin(x)|)}

as sin(x) belongs to [-1,1] so {log|sin(x)|} is defined for all x except when sinx=0. as inside the log the value of sinx will vary frm 0 to 1 so log|sinx| will be a -ve number and log(-ve number) is not defined.

so,

the given function is not defined for any value of x. So it cannot be differentiated.

iitkgp_bipin

0<= |sinx| <= 1

Hence log(|sinx|) < 0

log{log(|sinx|)} is not defined for any value of x.

Hence it is a non-differentiable function.

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