`f(x) = cos(x^2), (0,1)` Evaluate the second derivative of the function at the given point. Use a computer algebra system to verify your result.
We will need to use chain rule
First we find the first derivative.
`f'(x)=-sin(x^2)cdot 2x=-2x sin(x^2)`
Now we calculate second derivative, but for that we will need to use the following formula
`(f cdot g)'=f' cdot g+f cdot g'`
Now we evaluate the second derivative at 0.
In the image below blue is the function and red is its second derivative.