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To differentiate an integral whose upper limit is $u=\sqrt{t}$, apply the chain rule by evaluating the continuous integrand at $u$ and multiplying by the derivative of the upper limit, $1/(2\sqrt{t})$. This process requires $t > 0$ to ensure the upper limit function is differentiable.

Conditions: The integrand is continuous on the relevant interval.; The upper limit is a differentiable function of $t$, specifically $u=\sqrt{t}$.; $t > 0$.

To differentiate an integral whose upper limit is $u=\sqrt{t}$, apply the chain rule by evaluating the continuous integrand at $u$ and multiplying by the derivative of the upper limit, $1/(2\sqrt{t})$. This process requires $t > 0$ to ensure the upper limit function is differentiable.

Conditions: The integrand is continuous on the relevant interval.; The upper limit is a differentiable function of $t$, specifically $u=\sqrt{t}$.; $t > 0$.