Consider the derivative of: $$I(x)x*I(x)x^3$$ Where $I(x)$ is the indicator function on $[-1,1]$.
One way to evaluate it gives $I(x)*I(x)x^3$ and the other way gives $3I(x)x* I(x)x^2$ but these two expressions are not equal. Here I am using the convolution property $(f*g)' = f'*g$ and commutativity of the convolution operator.
I'm struggling to see how the $2$ answers can be equal. Where am I going wrong?