In Exercises JJ- 24, a matri,r and " scalar !.. are given. Show that !.. is an eigenvalue of tile mmrix and detumine a basis for [19 -~am its eigenspace. 15. -11-3

Calculus 3 Week 4: Partial Derivatives ' Recall that the derivative f (x) represents the rate of change of the function as x changes. When we have partial derivatives, it just means we have more than one variable to keep track of. We will treat the other variables as constants while we differentiate the function with respect to the variable in question. Examples 2 a) f(x ,y)=3x+2y Let’s first differentiate with respect to . Remember we treat y as a constant. ∂x =3 ∂ f That’s it! Yes! Remember, constants have derivatives of zero! Now let’s differentiate with respect to y , treating x as