Hi all. I am looking at the functions [itex]\tau(x,y)[/itex], [itex]T(x,y)[/itex], and [itex]R(T)[/itex] related by(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \tau(x,y) = \int_{\pi}^{T(x,y)} R(\theta) d\theta .[/tex]

It seems that by Leibniz's integral rule

[tex] \frac{\partial \tau}{\partial x} = \int_\pi^{T} \frac{\partial R}{\partial x} d\theta + R(T)\frac{\partial T}{\partial x}. [/tex]

It seems that [itex]\partial R / \partial x [/itex] need not be zero, yet another resource tells me that

[tex] \frac{\partial \tau}{\partial x} = R(T)\frac{\partial T}{\partial x} .[/tex]

Have I gone wrong somewhere? Thanks!

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# Derivative by Leibniz's integral rule

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