Hi, I'm very confused about these:
1. y=2^ln x
2. y=ln2^x
for #1, wouldn't it be:
y=2^ln x
y'=ln x (2^ln x) (ln 1/x) ?
but the answer in the book says it's y'=ln x (2^ln x) (1/x).
and I have absolutely no idea how to begin #2.
edit:
sorry, but these too:
3. f(x) = Ae^-Bx
book says f'(x) = Ae^-Bx (-B). I don't understand where would the -Bx go
4. f(x) = L/(1+Ae^-Bx)
thank you so much in advance!
I would suggest you NOT use that property as it isn't true! The correct property is . Write and use the chain rule: the derivative is times the derivative of u ln(a) with respect to u which is ln(a), not ln(u).
The derivative of is, by the chain rule, again, times the derivative of ln(x) which is 1/x. The derivative of is so your book (believe it or not!) is correct.a = 2, u = ln(x)
Perhaps 1/ln(x) is obtained from the chain rule but I don't see it.
Exactly right!For number 2 use the property of logs that says
This should be easy to differentiate. Remember ln(2) is a constant