Solve \left\{\begin{array}{l} {x=3\sin t}\\{y=2\cos t

求值

{x = 3 sin (t) y = 2 cos (t)

求导数 \frac{d y}{d x} ，先求 \frac{d x}{d t} 和 \frac{d y}{d t}

\frac{d}{d t} (x) = \frac{d}{d t} (3 sin (t)) \frac{d}{d t} (y) = \frac{d}{d t} (2 cos (t))

求导数

More Steps

\frac{d x}{d t} = 3 cos (t) \frac{d}{d t} (y) = \frac{d}{d t} (2 cos (t))

求导数

More Steps

\frac{d x}{d t} = 3 cos (t) \frac{d y}{d t} = - 2 sin (t)

通过将 \frac{d x}{d t} = 3 cos (t) 和 \frac{d y}{d t} = - 2 sin (t) 代入 \frac{d y}{d x} = \frac{\frac{d y}{d t}}{\frac{d x}{d t}} 找到所需的导数

\frac{d y}{d x} = \frac{- 2 sin ( t )}{3 cos ( t )}

Solution

\frac{d y}{d x} = - \frac{2 sin ( t )}{3 cos ( t )}

\left\{\begin{array}{l} {x=3\sin t}\\{y=2\cos t}\end{array}\right.