Which f the following statements is true
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Which f the following statements is true

[From: ] [author: ] [Date: 12-06-12] [Hit: ]
y)= g(x) + h(y),Can someone help me with this, I know its partials so im thinking a or d??-It is d.Note that differentiating with respect to one variable treats the other variable as a constant.......
a) if f(x,y) = g(x)*h(y), then f_xy = 0
b) if f(x,y)= g(x) + h(y), then f_xy = g'(x) + h'(y)
c) if f(x,y)= g(x)*h(y), then f_xy = g'(x)*h(y) + g(x)*h'(y)
d) if f(x,y)= g(x) + h(y), then f_xy = 0
e) if f(x,y)= g(x) + h(y), then f_xy = g'(x)*h'(y)

Can someone help me with this, I know its partials so im thinking a or d??

-
It is d.

Note that differentiating with respect to one variable treats the other variable as a constant. Also, to find f_{xy}, you can first differentiate with respect to x, and then differentiate the result with respect to y. Let's take derivatives assuming some of the choices:

a) Suppose f(x,y) = g(x)h(y). Then:

f_x = g'(x)h(y)
f_{xy} = d/dy[g'(x)h(y)]= g'(x)h'(y).

b) Suppose f(x,y) = g(x) + h(y). Then:

f_x = g'(x)
f_{xy} = d/dy [g'(x)] = 0

c) We already computed this in part (a).

d) We already computed this in part (b).

e) We already computed this in part (b).
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