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