Find dy/dx, if x=9t⁴ and y=t

The correct option is 1/36t³.

To find the derivative dydx when x and y are given parametrically in terms of t, we use the chain rule for parametric equations:
dydx=(dydt)(dxdt)

Step 1: Differentiate x with respect to t.
Given: x=9t4
Using the power rule of differentiation (ddt(tn)=ntn-1):
dxdt=9×4t3=36t3

Step 2: Differentiate y with respect to t.
Given: y=t
Differentiating with respect to t gives:
dydt=1

Step 3: Substitute the derivatives into the parametric formula.
Now we substitute the expressions we found for dydt and dxdt:
dydx=136t3

This matches the correct option 1/36t³.