In an numerical analysis project I need as an intermediate step to calculate the following: $$\max_{0\leq x\leq3} |f'(x)|,\ \ \max_{0\leq x\leq3} |f''(x)|\ \ \text{and}\ \ \max_{0\leq x\leq3} |f^{(4)}(x)|$$
Where $f(x)=\sin(\cos(\sin(\cos(x^2))))$
I tried using Wolfram Alpha to find the maximum of each function but it says "No global maximum found". I tried using Maxima but I couldn't find the value for those either. Maybe this is because the expression for the derivatives gets very big due to all the nested trig. functions.
How can I numerically find these values? What are some other tools/software that can handle this?