Answer
$$f_x = \frac{ln \space t}{2 \sqrt x}$$ $$f_t =\frac{\sqrt x}{t}$$
Work Step by Step
$$f(x,t) = \sqrt x \space ln\space t$$ $$f_x = (\frac 1{2\sqrt x} )(ln \space t)$$
$ln \space t$ is constant.
$$f_t = \sqrt x \space \frac 1t = \frac{\sqrt x}{t}$$
$\sqrt x$ is constant.
