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Use the following table to evaluate Dx[xg(x)+g(f(x))] at x=3

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Use the following table to evaluate Dx[xg(x)+g(f(x))] at x=3

X=1 X=2 X=3

g(x) 3 6 4

g'(x) -4 -1 -1 

f(x) 1 -1 1

f'(x) -8 0 2

Apr 27th, 2015

D(x)=[x(xg+g(f))]'= [x^2*g+x*g(f)]'=2x*g+x^2*g'+g(f)+xg'(f)*f'

at x= 3: g=4, g'=-1,  f=1, f'=2, g(f)=g(1)=3, g'(f)=g'(1)=-4

D(3)= 2*3*4+9*(-1)+3+3*(-4)*2 = 24-9+3-24= - 6


Apr 27th, 2015

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