Definition of Derivative! (Please Help!)

Alextu

New member
Joined
Dec 16, 2019
Messages
1
Hey

I need urgent help with the following question:

Show that f’(x)= -1/2 by using the derivative function, And the power series expansion

f(x)=(x-x^2+x^3/4)/ln(1+x)

Would be great with a step by step answer!
 
Please state the entire problem you are working on, exactly as given to you, and the context (what you have been learning).

Are you supposed to use the definition of the derivative (as in your title), or a power series expansion (as in your question)?

And how can the derivative of a non-linear function be a constant? There's something missing here.
 
Would be great with a step by step answer!
That is what just what we do here. We help the student answer their question in a step by step fashion. Can you please show us the steps you did so we can tell you if they are correct or not and give you some hints.
 
You title this "Definition of Derivative!". Are you required to use the definition of the derivative: \(\displaystyle f'(x)= \lim_{h\to 0}\frac{f(x+h)- f(x)}{h}\) (which would be very difficult) or can you use more advanced methods, like the "quotient rule" (which would be comparatively easy)?

Also, how are we to interpret "x-x^2+x^3/4"? As it is written, I would say it is \(\displaystyle x- x^2+ \frac{x^3}{4}\) but people often forget parentheses. It is possible that you meant "(x- x^2+ x^3)/4" which would be \(\displaystyle \frac{x- x^2+ x^3}{4}\) or "x- x^2+x^(3/4)" which would be \(\displaystyle x- x^2+ x^{3/4}\).
 
Top