What would you like to understand?

To differentiate an integral with a square-root upper limit, you evaluate the integrand at the upper limit and multiply by the derivative of that limit. For an upper limit $u=\sqrt{t}$, the derivative is $1/(2\sqrt{t})$.

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 with a square-root upper limit, you evaluate the integrand at the upper limit and multiply by the derivative of that limit. For an upper limit $u=\sqrt{t}$, the derivative is $1/(2\sqrt{t})$.

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