Past exam of the options II course of the University of Oxford / 2011 / F / F2 / b / iii

The total derivative of $g$ sends a scalar increment $s$ toSince ${\sin }^{2}t+{\cos }^{2}t=1$, the function composition $f\circ g$ is constantly $1/2$, so $D(f\circ g)(t)=0$. Directly, the Jacobian matrix product isThis verifies the chain rule at every $t$.