Question

Помогите с производными пж

Answer 1

Ответ:

$\left\{\begin{array}{l}x=sin2t\\y=t\, sin2t-sin^2t\end{array}\right\\\\\\x'_{t}=2\, cos2t\\\\y'_{t}=sin2t+2\, t\cdot cos2t-\underbrace{2sint\cdot cost}_{sin2t}=2t\cdot cos2t\\\\\\y'_{x}=\dfrac{y'_{t}}{x'_{t}}=\dfrac{2t\cdot cos2t}{2\, cos2t}=t=\dfrac{1}{2}\, arcsinx\\\\\\y''_{tt}=(2t\cdot cos2t)'=2\, cos2t+2t\cdot (-2sin2t)=2\cdot (cos2t-2t\, sin2t)\\\\y''_{xx}=\dfrac{cos2t-2t\, sin2t}{cos2t}=1-2t\cdot tg2t$