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??
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??
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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).
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).