Question

if f(x)= loga log lx), then f'(x) is​

Answer 1

Answer:

Step-by-step explanation:

As an high school student, I don't use logx=lnx but most mathematicians do. So I solved it in terms of logx=log10x and found logee=1ln(e).e instead of 1e. Anyway, here's the solution:

f(x)=log(log(x))

f(x)=logx

f′(x)=(x)′ln(10).x=1ln(10).x

hence

f′(x)=(logx)′logx.loge

f′(x)=1x.logelogx.loge

f′(x)=1x.log2elogx

f′(x)=log2ex.logx

for x=e,

f′(e)=log2ee.loge

f′(e)=logee

or

f′(e)=1ln10.e