Given that x=ln(t) and y=4t^3,a) find an expression for dy/dx, b)and the value of t when d2y/dx2 =0.48. Give your answer to 2 decimal place.
a) Firstly, differentiate x and y with respect to t.
Giving you dx/dt = 1/t and dy/dt = 12t2
dy/dx is found using the chain rule:
dy/dx = dy/dt x dt/dx = 12t3
b) You will need to differentiate dy/dx again with respect to t, to do this:
d2y/dx2=36t2 x dt/dx = 36t3
36t3=0.48
t=(0.48/36)1/3
t=0.24
