Question

Найти производную dz/dt, если z=e^2y-3x, x=tgt, y=t-t^2

Answer 1

$\frac{dz}{dt}-?$

$z=e^{2y}-3x,x=tgt,y=t-t^2\\z=e^{2(t-t^2)}-3*tgt\\\frac{dz}{dt}=(e^{2(t-t^2)}-3tgt)'=e^{2(t-t^2)}*(2t-2t^2)'-\frac{3}{cos^2t}=e^{2(t-t^2)}(2-4t)-\frac{3}{cos^2t}$