【高校数学Ⅲ】3-1-7 曲線方程式の微分法｜問題集

両辺を\(x\)で微分すると、
\(\displaystyle 2x+\frac{dy}{dx}2y=0\)
\(\displaystyle \frac{dy}{dx}=-\frac{x}{y}\)

両辺を\(x\)で微分すると、
\(\displaystyle 2x-\frac{dy}{dx}2y=0\)
\(\displaystyle \frac{dy}{dx}=\frac{x}{y}\)

\(\displaystyle \frac{dx}{dt}=2t\)
\(\displaystyle \frac{dy}{dt}=3t^2\)
\(\displaystyle \frac{dy}{dx}=\frac{3t^2}{2t}=\frac{3}{2}t\)

\(\displaystyle \frac{dx}{dt}=4t\)
\(\displaystyle \frac{dy}{dt}=2\)
\(\displaystyle \frac{dy}{dx}=\frac{2}{4t}=\frac{1}{2t}\)

\(\displaystyle \frac{dx}{dt}=-\sin t\)
\(\displaystyle \frac{dy}{dt}=\cos t\)
\(\displaystyle \frac{dy}{dx}=-\frac{\cos t}{\sin t}\)