При параметрическом задании функции
du/dt = du/dx*dx/dt + du/dy*dy/dt
3124. u = e^(x - 2y); x = sin t; y = t^3
du/dx = e^(x - 2y); du/dy = e^(x - 2y)*(-2) = -2e^(x - 2y)
dx/dt = cos t; dy/dt = 3t^2
du/dt = du/dx*dx/dt + du/dy*dy/dt =
= e^(x - 2y)*cos t - 2e^(x - 2y)*3t^2 =
= e^(sin t - 2t^3)*(cos t - 6t^2)
3125. u = z^2 + y^2 + zy; z = sin t; y = e^t
du/dz = 2z + y; du/dy = 2y + z
dz/dt = cos t; dy/dt = e^t
du/dt = du/dz*dz/dt + du/dy*dy/dt =
= (2z + y)*cos t + (2y + z)*e^t =
= (2sin t + e^t)*cos t + (2e^t + sin t)*e^t