Find d^2 y/dx^2

[sareen]

X= 2t^3 -6t
Y=t+1
?dy/dx= 1/ 6(t^2 -1)
?d/dt(dy/dx)/(dx/dt)= d/dt(1/ 6(t^2 -1))/6t^2-1
What’s the next step?



Thank you for helping!!!

 

[chrisr]

You are calculating (1/6)d/dt(1/(t[sup:8ect1sm2]2[/sup:8ect1sm2]-1)) and dividing that by the denominator you've written.
So the next step is to differentiate 1/(t[sup:8ect1sm2]2[/sup:8ect1sm2]-1) with respect to t.

You can either say that this is d/dt(t[sup:8ect1sm2]2[/sup:8ect1sm2]-1)[sup:8ect1sm2]-1[/sup:8ect1sm2]
or use the "quotient rule of differentiation".