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I have the function

$$f(t) = \int_0 ^{t} \frac{1}{\sqrt{t-\tau}} \mathrm{d}\tau$$

The integral can be found, yielding an expression as

$$f(t) = 2 \sqrt{t} $$

The question is, if I tried to calculate the derivative of $$f$$, using the "derivation under the integral " rule I get

$$\frac {\mathrm{d} f }{\mathrm{d}t} = \int_0 ^{t} \frac{\mathrm{d}}{\mathrm{d}t} \frac{1}{\sqrt{t-\tau}} \mathrm{d}\tau + \frac{1}{\sqrt{t-t}} $$

which is a problem I never run across.

I went through the derivation of the "derivation under the integral " but I am not getting anywhere, for the moment.

Anybody's help would be appreciated, thanks

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# Derivative of an integral function

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