Question

Найдите производную dz/dt функции z=arccos(x+y), x=3t, y=4t^3. Решите плизз))

Answer 1

$x=3t; ,; ; y=4t^3\\z=arccos(x+y)=arccos(3t+4t^3)\\z'_{t}=frac{dz}{dt}=-frac{1}{sqrt{1-(3t+4t^3)^2}}cdot (3+12t^2)\\ili\\frac{dz}{dt}=frac{partial z}{partial x}cdot frac{dx}{dt}+frac{partial z}{partial y}cdot frac{dy}{dt}\\frac{dz}{dt}=-frac{1}{sqrt{1-(x+y)^2}}cdot 3-frac{1}{sqrt{1-(x+y)^2}}cdot 12t^2=-frac{1}{sqrt{1-(x+y)^2}}cdot (3+12t^2)=\\=-frac{1}{sqrt{1-(3t+4t^3)^2}}cdot (3+12t^2)$