Help!!!!
The d/dx of log x = 1/x. the d/dx of log -x is now what please? it cant be 1/x can it
+33661 Yes it can!
ln(-x) = ln(x) + ln(-1) → ln(x) + i*pi (where i= sqrt(-1))
i*pi is a constant hence d ln(-x)/dx = d ln(x)/dx → 1/x
Possible derivation:
d/dx(log(-x))
Using the chain rule, d/dx(log(-x)) = ( dlog(u))/( du) ( du)/( dx), where u = -x and ( d)/( du)(log(u)) = 1/u:
= -(d/dx(-x))/x
Factor out constants:
= --d/dx(x)/x
Simplify the expression:
= (d/dx(x))/x
The derivative of x is 1:
Answer: | = 1/x
