Let x(t)=t−sin⁡(t)\displaystyle {x}{\left({t}\right)}={t}-{\sin{{\left({t}\right)}}}

and y(t)=1−cos⁡(t)\displaystyle {y}{\left({t}\right)}={1}-{\cos{{\left({t}\right)}}}

At t=5\displaystyle {t}={5},

x(5)=\displaystyle {x}{\left({5}\right)}=  
y(5)=\displaystyle {y}{\left({5}\right)}=  

dxdt∣t=5=\displaystyle \frac{{{\left.{d}{x}\right.}}}{{{\left.{d}{t}\right.}}}{\mid}_{{{t}={5}}}=  

dydt∣t=5=\displaystyle \frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{t}\right.}}}{\mid}_{{{t}={5}}}=  

dydx∣t=5\displaystyle \frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}{\mid}_{{{t}={5}}} = tangent slope =  

speed(5) =\displaystyle \text{speed(5) =}  

License