Answer
cox(t) = $3(4-6t)^{2}-2$
Derivative of this function is -144+216t.
Work Step by Step
c(x(t))= c(4-6t)= $3(4-6t)^{2}-2$
Let $3(4-6t)^{2}-2$= y and 4-6t= u
Then, y= $3u^{2}-2$
$\frac{dy}{du}$= 6u and $\frac{du}{dt}$= -6
According to the chain rule $\frac{dy}{dt}=\frac{dy}{du}.\frac{du}{dt}= 6uĆ(-6)$
Substituting the value of u, we obtain
$\frac{dy}{dt}= 6(4-6t)(-6)= -36(4-6t)= -144+216t$ which is the required derivative.