Question

Найдите производную функции, заданную неявно:
$e^{x}cosy- e^{-x}siny=0$

Answer 1

$e^{x}cos y- e^{-x}sin y=0 \ (e^{x}cos y)'- (e^{-x}sin y)'=0' \ (e^{x})'cos y+e^{x}(cos y)'-(e^{-x})'sin y-e^{-x}(sin y)'=0 \ e^{x}cos y+e^{x}(-sin y)cdot y'-(-e^{-x})sin y-e^{-x}cos ycdot y'=0 \ e^{x}cos y-e^{x}sin ycdot y'+e^{-x}sin y-e^{-x}cos ycdot y'=0 \ e^{x}sin ycdot y'+e^{-x}cos ycdot y'=e^{x}cos y+e^{-x}sin y \ y' (e^{x}sin y+e^{-x}cos y)=e^{x}cos y+e^{-x}sin y \ y'= dfrac{e^{x}cos y+e^{-x}sin y}{e^{x}sin y+e^{-x}cos y}$