How do you use the derivative to find the slope of a curve at a point?

If $f ' \left(x\right)$ is the derivative of $f \left(x\right)$, input the x value of the point to f'(x).
Say you have $f \left(x\right) = {x}^{2}$, then the derivative is $f ' \left(x\right) = 2 x$.
To find the slope of ${x}^{2}$ at the point (3,9), put the x value of the point into the derivative: $f ' \left(3\right) = 2 \cdot 3 = 6$.