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\end{equation}  Likewise we can find $\d/d\mathbb{I} $d/d\mathbb{I}  cos(x) = -xsin(x)$. Which is making the results look suspiciously like $x$ times the 'regular derivative'. Just going by the rule that we times the factor $(1-\delta)$ to any occurence of $x$ in the function would leave the derivative of a constant as $0$ still, (which would indeed be $x$ times the regular derivative). However, the first integral shown, the right hand side had the derivative taken, this scenario needs to be protected or contradication will occur!