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Given y = f(u) and u = g(x), find dy/dx = f’(g(x))g’(x)

Given y = f(u) and u = g(x), find dy/dx = f’(g(x))g’(x)-example-1

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Answer:


Given ~that:-


y=f(u)\\


and~u=g(x)


So, dy/dx=f'(g(x))g'(x)


Now, y=u(u-1)


So, f(u)=4(4-1)


u=x^2+x


so,g(x)=x^2+x


d/dx=(g(x))=2x+1


g'(x)=2x+x


f(x)g'(x)=(x^2+x)(x^2+x-1)


f(g(x))g'(x)=x^2(x^2+x-1)+x(x^2+x-1)


=x^4+x^3-x^2+x^3+x^2-x


f(g(x)g'(x)=x^4+2x^3-x

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So, ~ your~ answer~ is~ (B)~f'(g(x))g'(x)=4x^3+6x^2-1

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hope it helps...

have a great day!!

User Harry Binswanger
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