(Solved): Consider the following. \[ \begin{array}{ll} \text { Function } & \text { Point } \\ y=\frac{8+\csc ...

Consider the following. \[ \begin{array}{ll} \text { Function } & \text { Point } \\ y=\frac{8+\csc (x)}{7-\csc (x)} & \left(\frac{\pi}{6}, 2\right) \end{array} \] Find the derivative of the function. \[ y^{\prime}= \] Find \( y^{\prime}(x) \) when \( x=\frac{\pi}{6} \) \[ y^{\prime}\left(\frac{\pi}{6}\right)= \] Find the slope of the graph of the function at the given point \( \left(\frac{\pi}{6}, 2\right) \). Use the derivative feature of a graphing utility to confirm your resu Determine the point at which the graph of the function has a horizontal tangent line. \[ f(x)=\frac{2 x-3}{x^{2}} \] Find the given higher-order derivative. \[ f^{(3)}(x)=\sqrt[6]{x^{5}}, f^{(4)}(x) \] \[ f^{(4)}(x)= \]