Question $5$

Consider the function $f(x)=(2x^3-x{)}^6.To$ compute $f^{\text{'}}(x),we$ use the chain

rule for $f(x)=(g(x){)}^6,$ where $g(x)=2x^3-x.$

$We$ express the derivative using the formula $f^{\text{'}}(x)=6(g(x){)}^5*g^{\text{'}}(x).$ The

derivative $is$

$f^{\text{'}}(x)=6(2x^3-x)*(6x^2-1)$

$f^{\text{'}}(x)=(2x^3-x{)}^6*(6x^2-1)$

$f^{\text{'}}(x)=6(6x^2-1{)}^5$

$f^{\text{'}}(x)=6(2x^3-x{)}^5*(6x^2-1)$