Find dy/dx ??

Question

Given the parametric equations x = f(t) and y = g(t), dy/dx is given by g'(t)/f'(t). Find dy/dx given parametric equations below.

 

dy/dx=(g^′ (t))/(f^′ (t) )

 

Parametric equations:
x=(t+1)/2

y=−t^2+t

 

Answer 1

Hi Daniel, 

x = f(t), y =g(t)

dy/dx= g′(t)/ f′(t) 
Parametric equations:
x=(t+1)/2, 

dx/dt = 1/2, but x = f(t) then dx/dt = f'(t)

f'(t) = 1/2
y=−t^2+t

dy/dt = -2t + 1, since y = g(t), dy/dt = g'(t)

g'(t) = -2t + 1 

 

dy/dx = g'(t)/f'(t)

         = (-2t+1)/(1/2)

         =2(-2t +1)

dy/dx = 2(1 - 2t)