Learn If X 3t2 And Y 6t Then What Is Dy Dx

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# If x = 3t^{2} and y = 6t, then what is dy/dx?

**Solution:**

x and y are the parametric functions with the parameter t.

Hence my parametric differentiation, we have dy/dx = dy/dt . dt/dx

dy/dt = d(6t)/dt = 6

dx/dt = d(3t^{2})/dt = 6t

dy/dx = (dy/dt) / dx/dt = 6/6t

**dy/dx **=** 1/t**

Let us take another example where

x = t^{2} - 2t and y = t^{4} - 4t

dx/dt = 2t - 2 = 2(t - 1)

dy/dt = 4t^{3} - 4 = 4(t^{3} - 1)

dy/dx = (dy/dt) / dx/dt = 3(t^{3} - 1) / 2(t + 1) = (3(t - 1)(t^{2} + t + 1)) / 2(t-1)

= (3/2)(t^{2} + t + 1)

## If x = 3t^{2} and y = 6t, then what is dy/dx?

**Summary:**

If x = 3t^{2} and y = 6t, then dy/dx is 1/t

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