Question

Find the second derivative of the parametric equation.

Answer 1

Parametric Equation: x=9t, y=6t-8
I got dy/dx = \[4/((1/2)t ^{-1/2})\]

Now I need to find d^2y/dx^2. And I got \[-t ^{-3/2}/((1/2)t ^{-1/2})^3\]

But It says that I got it wrong. Where did I go wrong?

Answer 2

wouldn't dy/dx = 2/3

\[\frac{dy}{dx} = \frac{dy}{dt}*\frac{dt}{dx} = 6*\frac{1}{9} = \frac{2}{3}\]

Answer 3

I would have used substitution

t = x/9

then y = 6(x/9) - 8

dy/dx = 2/3

then 2nd derivative

d^y/dx^2 = 0

Answer 4

How did you get:
dy/dx =
4/((1/2)t−1/2)?