Question

x=e^t, y=sint, z=x^2+xy

dz/dt = ???

Answer 1

Solution;

Given;

$x=e^t$

$x^2=e^{2t}$

Also;

$y=sin t$

Hence:

$z=e^{2t}+e^{t}sint$

Differentiate by applying product rule;

$\frac{dz}{dt}=2e^{2t}+e^tcost+e^tsint$