D) find the 5th degree taylor polynomial centered at x = 0 for the function y = \tiny \frac{x}{1+x}

Step-by-step explanation:

Let us first remember how a Taylor polynomial looks like:

Given a differentiable function then we can find its Taylor series to the degree as follows:

Where represents the Remainder and is the derivative of .

So let us find those derivatives.

The only trick for this derivatives is for the very first one:

Then it's only matter of replacing on the Taylor Series and replacing