### Example Problem on Gradient and Directional Derivative Let \( f(x, y) = xe^{x^2 - y} \) and \( P = (13, 169) \). #### 1. Calculate \( \| \nabla f_p \| \). (Express numbers in exact form. Use symbolic notation and fractions where needed.) \[ \| \nabla f_p \| = \] --- #### 2. Find the rate of change of \( f \) in the direction \( \nabla f_p \). (Express numbers in exact form. Use symbolic notation and fractions where needed.) The rate of change: \[ \text{the rate of change:} \ \boxed{} \] --- #### 3. Find the rate of change of \( f \) in the direction of a vector making an angle of \( 45^\circ \) with \( \nabla f_p \). (Express numbers in exact form. Use symbolic notation and fractions where needed.) The rate of change: \[ \text{the rate of change:} \ \boxed{} \]

Give an example of a increased rate and a decreased rate

Use a right triangle to write csc(arccos(3*x/2)) as an expression of x that does not involve trig or inverse trig functions.

simplyfy to one trig function tan^2 B csc^B