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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
