Question

How do you differentiate the following parametric equation: `(3sin(t/6-pi/12), 2tcos(pi/3-t/8))`?

Answer 1

`dx/dt=1/2 cos(t/6-pi/12)`
`dy/dt=2{cos(pi/3-t/8)+t/8sin(pi/3-t/8)}`

Explanation:

`x=3sin(t/6-pi/12)`
`dx/dt=3(1/6)cos(t/6-pi/12)=1/2 cos(t/6-pi/12)`

`y=2tcos(pi/3-t/8)`
`dy/dt=2{cos(pi/3-t/8)d/dt(t)+td/dt(cos(pi/3-t/8)}`
`dy/dt=2{cos(pi/3-t/8)*(1)-t(-1/8)sin(pi/3-t/8)}`

`dy/dt=2{cos(pi/3-t/8)+t/8sin(pi/3-t/8)}`