Mathematics, 17.01.2020 20:31 1969976289
Find the derivative of f (x)=(x^2+1)^3 (x^2+2)^6 using chain rule.
Answers: 1
![\bf f(x)=(x^2)^3(x^2+2)^6\impliedby \textit{product rule on the factors} \\\\\\ \cfrac{df}{dx}=[ 3(x^2+1)^2(2x)][(x^2+2)^6]~+~(x^2+1)^3[6(x^2+2)^5(2x)] \\\\\\ \cfrac{df}{dx}=[6x(x^2+1)^2(x^2+2)^6]~+~[12x(x^2+1)^3(x^2+2)^5] \\\\\\ \cfrac{df}{dx}=\stackrel{\textit{common factor}}{6x(x^2+1)^2(x^2+2)^5}[(x^2+2)+2(x^2+1)] \\\\\\ \cfrac{df}{dx}=6x(x^2+1)^2(x^2+2)^5[3x^2+4]](/tpl/images/0459/6934/679b2.png)
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Find the derivative of f (x)=(x^2+1)^3 (x^2+2)^6 using chain rule....
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