Sebastian M. answered • 12d

Experienced HS/College Tutor for Math and Standardized Tests

One cool way to do this problem is to take the derivative of u(t^4-2t) using the chain rule:

d/dt u(t^{4}-2t) = u'(t^{4}-2t)*(4t^{3}-2)

Using the derivative equation you calculated, we can get a solution for u'(t^{4}-2t)

u'(t)=18t^2**i**+2t**j** => u'(t^{4}-2t) = 18(t^{4}-2t)^{2}**i**+2(t^{4}-2t)**j**

So finally then putting it all together:

d/dt u(t^{4}-2t) = (4t^{3}-2)[18(t^{4}-2t)^{2}**i**+2(t^{4}-2t)**j**]