Question

Найти производные функций, заданных параметрически:

Answer 1

Ответ:

$\left\{\begin{array}{l}y=arcsint\\x=\sqrt{1-t^2}\end{array}\right\ \ \ \ ,\ \ 1-t^2=x^2\ \ ,\ \ t^2=1-x^2\ \ ,\ \ t=\sqrt{1-x^2}\\\\\\y'_{t}=\dfrac{1}{\sqrt{1-t^2}}\\\\\\x'_{t}=\dfrac{1}{2\sqrt{1-t^2}}\cdot (-2t)=\dfrac{-t}{\sqrt{1-t^2}} \\\\\\y'_{x}=\dfrac{y'_{t}}{x'_{t}}=\dfrac{\frac{1}{\sqrt{1-t^2}}}{\frac{-t}{\sqrt{1-t^2}}}=-\dfrac{1}{t}=-\dfrac{1}{\sqrt{1-x^2}}$