Question

Pamagiti
z=y/x, x=e^t, y=1-e^2t; найти dz/dt

Answer 1

$\frac{dz}{dt} = \frac{dz}{dx} \times \frac{dx}{dt} + \frac{dz}{dy} \times \frac{dy}{dt}$

$\frac{dz}{dx} = - y {x}^{ - 2} = - \frac{y}{ {x}^{2} }$

$\frac{dx}{dt} = {e}^{t}$

$\frac{dz}{dy} = \frac{1}{x}$

$\frac{dy}{dt} = - 2 {e}^{2t}$

$\frac{dz}{dt} = - \frac{y}{ {x}^{2} } {e}^{t} - \frac{ 2{e}^{2t} }{x}$