Property 13
Derivative of Parametric Function
\(y=f(t)\)
\(x=h(t)\)
\(\boxed{\samefrac{dy}{dx}=\samefrac{\samefrac{dy}{dt}}{\samefrac{dx}{dt}}}\)
1.
\(y=2t^2-2\)
\(x=3t\)
\(\Rightarrow \left.\samefrac{dy}{dx}\right|_{t=2}=?\)
2.
\(y=2m^2-3m\)
\(x=3m^2\)
\(\Rightarrow \left.\samefrac{dy}{dx}\right|_{m=1}=?\)
3.
\(y=\cos t\)
\(x=\sin t\)
\(\Rightarrow \left.\samefrac{dy}{dx}\right|_{t=\samefrac{\pi}{4}}=?\)
4.
\(y=3^t\)
\(x=\sin t\)
\(\Rightarrow \left.\samefrac{dy}{dx}\right|_{t=0}=?\)
5.
\(y=\ln t^2\)
\(x=t^3\)
\(\Rightarrow \left.\samefrac{dy}{dx}\right|_{t=2}=?\)
6.
\(y=t^2-1\)
\(x=\arctan t\)
\(\Rightarrow \left.\samefrac{dy}{dx}\right|_{t=2}=?\)
7.
\(y=t^3-1\)
\(x=\sqrt t\)
\(\Rightarrow \left.\samefrac{dy}{dx}\right|_{t=4}=?\)