Answer:
[tex]Given ~that:-[/tex]
[tex]y=f(u)\\[/tex]
[tex]and~u=g(x)[/tex]
[tex]So, dy/dx=f'(g(x))g'(x)[/tex]
[tex]Now, y=u(u-1)[/tex]
[tex]So, f(u)=4(4-1)[/tex]
[tex]u=x^2+x[/tex]
[tex]so,g(x)=x^2+x[/tex]
[tex]d/dx=(g(x))=2x+1[/tex]
[tex]g'(x)=2x+x[/tex]
[tex]f(x)g'(x)=(x^2+x)(x^2+x-1)[/tex]
[tex]f(g(x))g'(x)=x^2(x^2+x-1)+x(x^2+x-1)[/tex]
[tex]=x^4+x^3-x^2+x^3+x^2-x[/tex]
[tex]f(g(x)g'(x)=x^4+2x^3-x[/tex]
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[tex]So, ~ your~ answer~ is~ (B)~f'(g(x))g'(x)=4x^3+6x^2-1[/tex]
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hope it helps...
have a great day!!
