Question

Найдите производную функции

Answer 1

$\left\{\begin{array}{ccc}x=6cos^3t\\y=2sin^3t\end{array}\right\\\\\\y'_{x}=\dfrac{y'_{t}}{x'_{t}}=\dfrac{6sin^2t\cdot cost}{-18cos^2t\cdot sint}=-\dfrac{sint}{3cost}=-\dfrac{1}{3}\cdot tgt\\\\\\y''_{xx}=\dfrac{y'_{x}}{x'_{t}}=\dfrac{-\frac{1}{3cos^2t}}{-18cos^2t\cdot sint}=\dfrac{1}{54\, cos^4t\cdot sint}$