How do you differentiate the following parametric equation: # x(t)=t-cos^2t, y(t)=tsint #?

Question

1448 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-23T13:15:25

#dy/dx=\frac{1+\sin2t}{\sin t+t\cos t}#

Given that

#x(t)=t-\cos^2t\ \ &\ \ \ y(t)=t\sint #

Now, differentiating w.r.t. #x# as follows

#dy/dx#

#=\frac{dy/dt}{dx/dt}#

#=\frac{d/dt(t-\cos^2t)}{d/dt(t\sin t)}#

#=\frac{d/dt(t)-d/dt(\cos^2t)}{td/dt(\sin t)+\sin t\d/dt(t)}#

#=\frac{1-2\cos t(-\sin t)}{t\cos t+\sin t}#

#=\frac{1+\sin2t}{\sin t+t\cos t}#