Chapter 4.3, Problem 159E

Find the indicated higher-order partial derivatives.

159. The law of cosines can be thought of as a function of three variables. Let x. v and $\theta$be two sides of any

triangle where the angle $\theta$is the included angle between the two sides. Then, $F\left(x,y,\theta \right)=x^2+y^2-2xy\cos \theta$gives the square of the third side of the triangle. Find $\frac{\partial F}{\partial \theta }$

and $\frac{\partial F}{\partial x}$ when x = 2. y = 3, and $\theta =\frac{\pi }{6}$ .