Question

What is the derivative of `f(t) = ((lnt)^2-t, tcost )`?

Answer 1

`((2lnt)/t - 1, cos t - tsint)`

Explanation:

Interpreting the problem statement as the derivative of a vector, where each component is a function of `t`. We can simply find the derivative of each of these functions independently.

The x component is `f_x(t) = (lnt)^2 - t`, so its derivative is:

`f_x'(t) = (2lnt)/t -1`

The y component is `f_y(t) = tcost`, and its derivative is:

`f_y'(t) = cos t - tsin(t)`

GOOD LUCK