How to find the derivative f(f(x))=lnx Find the derivative of F, (x)

How to find the derivative f(f(x))=lnx Find the derivative of F, (x)

This is the derivative of the composite function,
f(f(x))=lnx
Two side derivation
Get: F (f (x)) f ` (x) = 1 / X
Substitute f (f (x)) = LNX into the above formula
Get: F ` (x) = 1 / xlnx

On the problem of finding derivative How to find the derivative of FX = root sign (x-3) (x ≥ 3)? Is there any general formula? I haven't solved it for a long time!

F (x) = (x-3) ^ (1 / 2) (x ^ (1 / 2) represents the square of x)
f'(x)=(1/2)*[(x-3)^(1/2-1)]*(x-3)'
=1/[2√(x-3)]
√ indicates the root sign

This economic formula Mr= Δ TR / Δ What does Q mean? What do they represent? Say it in detail. Urgent ~ ~ thank you!

MR is the marginal income and the derivative of the total income tr. if you find the derivative of the total income function TR, it is the marginal income function
Δ TR and Δ Q refers to the increment of total revenue and the increment of output. Mr = Δ TR/ Δ Q or Mr = DTR / DQ, which is the calculation formula of marginal income Mr

What are the full names of TFC, TVC, TC, AFC, AVC, AC and MC in economics

Total fixed cost
Total variance cost
Total cost
Average.. ditto
Average..
Average..
Marginal cost

All formulas between FC VC AVC TC MC AC Q (Western Economics) RT

TC=FC+VC
AVC=VC/Q
MC= δ TC/ σ Q
AC=TC/Q

What fabrics are tr and TC respectively

Tr: terylene rayon polyester + rayon (viscose)
TC: terylene / cotton polyester + Cotton