Answer to Question #271909 in Calculus for Angel Nodado

Question #271909

Find the first and second derivatives of the following and simplify whenever possible:



x = 9t ^ 2 - 1 : y = 3t+1

1
Expert's answer
2021-12-19T14:27:27-0500

Let us find the first and second derivative of the following:


x=9t21,  y=3t+1.x = 9t ^ 2 - 1,\ \ y = 3t+1.


It follows that yx=ytxt=318t=16t.y_x'=\frac{y_t'}{x_t'}=\frac{3}{18t}=\frac{1}{6t}.


Then yx2=(16t)txt=16t218t=1108t3.y_{x^2}''=\frac{(\frac{1}{6t})_t'}{x_t'}=\frac{-\frac{1}{6t^2}}{18t}=-\frac{1}{108t^3}.



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