Find dy/dx. x = t / (9 + t) y = √(9 + t).

Solution:

We apply differentiation of parametric functions as x = f(t) and y = g(t)

Let us find dy/dx by finding dy/dt and dx/dt

dy/dx = dy/dt . dt/dx

x = t/(9 + t)

dx/dt = ((9+t)dt/dt - t(d9/dt + dt/dt))/ (9+t)²

=  ((9 + t)  - t(0 + 1)) / (9+t)²

=  9 + t - t / (9+t)²

=  9/(9+t)²

y = √9+t

dy/dt = (½)(1)1/(√9+t)

=  1/ 2((√9+t))          

dy/dx = (dy/dt)/(dx/dt)   =  1/(2(√9+t)) / 9/(9+t)²

=  (1/18)  × ((9 + t)²/ √(9+t))

dy/dx = (1/18)(9 + t)^3/2 

Find dy/dx. x = t / (9 + t) y = √(9 + t).

Summary: 

dy/dx = (1/18)(9 + t)^3/2 when  x = t / (9 + t)and   y = √(9 + t).