So I need to find the differential with respect to time of 4sec(theta)- Find dr/dt and d^2r/dt^2 of r=4sec(theta) please? The r(theta).
This is what I have tried- 4(sectan * d(theta)/dt) =dr/dt
4sectan(d^2theta/dt^2) + (4sec^3(dtheta/dt)+ 4sectan^2(theta/dt))ethers/dt? Which is second derivative
Is the above correct please?
Thank you
Assuming that you function has form $r=4\sec(\theta (t))$, then $$\dot r(t)=4\dfrac{d\sec(\theta)}{d\theta}\dfrac{d}{dt}\theta(t)=4\tan(\theta)\sec(\theta)\dot\theta(t)$$ $$\ddot r(t)=4\dfrac{d}{dt}[(\tan\theta\sec\theta)\dot\theta]=4\Big(\dfrac{d(\tan\theta\sec\theta)}{dt}\cdot\dot\theta+\dfrac{d\dot\theta}{dt}\cdot\tan\theta\sec\theta\Big)=$$ $$=4[(\sec^2\theta\sec\theta\cdot\dot\theta)+(\tan\theta\sec\theta\tan\theta\cdot\dot\theta)]\cdot\dot\theta+4\ddot\theta\cdot\tan\theta\sec\theta$$
