Vectorization is crucial for obtaining good performance with NumPy.
Derivatives can be calculated numerically with the finite-difference method as:
Construct 1D Numpy array containing the values of xi in the interval [0,π/2]
with spacing Δx=0.1. Evaluate numerically the derivative of sin in this
interval (excluding the end points) using the above formula. Try to avoid
for loops. Compare the result to function cos in the same interval.