Derivativation of definite integral
By Emma Valentine •
Having:
$f = \int_0^{n}{X_{(t)}dt} + X_{n}$
How can I find:
$\frac{\partial{f}}{\partial{n}} = ?$
Please note that the derivative is done with respect to one of the ends of the integral. (hope that's clear English)
Thanks!
$\endgroup$ 21 Answer
$\begingroup$By the fundamental theorem of calculus,
$$\frac{\partial}{\partial x}\left(\int_a^x g(t)dt\right) = g(x).$$ Use this theorem to differentiate the right side of the equation you gave and then solve for $\frac{\partial X}{\partial n}$ in terms of $\frac{\partial f}{\partial n}$ and $X(n)$.
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