Question $5$

$1$ pts

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

$f(z)=6(2x^3-z{)}^3*(6x^2-1)$

$f(z)=6(6x^2-1{)}^5$

$f(z)=6(2x^3-x)*(6x^2-1)$

$f(x)=(2x^3-x{)}^4*(6x^2-1)$