# Question: Let f Rn R For x Rn a Show that Deif a Dif a

Let f: Rn →R. For x€ Rn,

a. Show that Deif (a) = Dif (a)..

b. Show that Dtxf (a) = Dxf(a)..

c. If f is differentiable at , show that Dxf(a) = Df(a)(x) (a) and therefore Dx + yf(a) = Dxf (a) + Dyf (a)..

a. Show that Deif (a) = Dif (a)..

b. Show that Dtxf (a) = Dxf(a)..

c. If f is differentiable at , show that Dxf(a) = Df(a)(x) (a) and therefore Dx + yf(a) = Dxf (a) + Dyf (a)..

## Relevant Questions

Let f be defined as in Problem 2-4. Show that Dxf (0, 0) exists for all , but if g ≠ 0, , then Dx + yf (0,0) =Dxf (00 Dx + y f (0, 0) = Dx f (0 , 0) + Dyf (0, 0) Is not true for all x and all y.If f : Rn → R is differentiable and f (0) = 0, prove that there exist gi: Rn → R such that f (x) =Let f : R x R → R be differentiable. For each x € R defined gx: R → R By gx (y) = f(x,y). Suppose that for each x there is a unique y with gx1(y) =0; let c(x) be this y.Surrealism is a movement devoted to expressing in the conscious life, the workings of the unconscious mind. There are no rational controls on words or images.Read 6.13 The Love Song of J. Alfred Prufrock by T.S. Eliot. Describe J. Alfred Prufrock's personality. Is he an anti-hero? (pg. 72)Post your question