Slope of tangent line via power rule

Apply the power rule with $n = 3/2$: $f'(x) = \frac{3}{2}x^{3/2 - 1} = \frac{3}{2}x^{1/2}.$ This gives the general formula for the slope of the tangent line at any point $x$.

Substitute $x = 9$: $f'(9) = \frac{3}{2}\sqrt{9} = \frac{3}{2}(3) = \frac{9}{2}.$ So the slope of the tangent line at $x=9$ is $\frac{9}{2}$.