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# 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).

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