# Thread: Find the second derivative

1. ## Find the second derivative

x=4sin(t) and y=2cos(t). I found the first derivative to be -(1/2)tan(t). How do I find the second derivative?

2. Your first derivative is fine. To find the second derivative take the derivative of the the first derivative. It's a standard derivative $\displaystyle \dfrac{1}{2} \cdot \dfrac{d}{dt} \tan(t) = \dfrac{1}{2} \sec^2(t)$

3. $\displaystyle \displaystyle \frac{d^2y}{dx^2}= \frac{d}{dx}\frac{dy}{dx} = \frac{d}{dt}\frac{dy}{dx}\frac{dt}{dx}$

4. Originally Posted by boosays
x=4sin(t) and y=2cos(t). I found the first derivative to be -(1/2)tan(t). How do I find the second derivative?
$\displaystyle \displaystyle \frac{d}{dx} \left(\frac{\frac{dy}{dt}}{\frac{dx}{dt}}\right) = \frac{d}{dt} \left(\frac{\frac{dy}{dx}}{\frac{dx}{dt}}\right)$

$\displaystyle \displaystyle \frac{d}{dt} \left(\frac{-\tan{t}}{8\cos{t}}\right)$

do the quotient rule to finish ...