AP Calculus BC / Parametric Equations, Polar Coordinates, and Vector-Valued Functions / Question No. 30

30. If \( x = 3t^2 - 1 \) and \( y = \ln t \), what is \( \frac{d^2y}{dx^2} \) in terms of \( t \)?

\(\frac{1}{6} t^2\)

\(-\frac{1}{3} t^{-3}\)

\(-\frac{1}{18} t^{-4}\)

\(-\frac{1}{2} t^{-4}\)

Answer is: option3

\(-\frac{1}{18} t^{-4}\)

Solution:

\(-\frac{1}{18} t^{-4}\)

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Home Practice Questions AP Calculus BC Parametric Equations, Polar Coordinates, and Vector-Valued Functions Question No. 30