Question

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

Answer 1

f'(t) = `((2 ln t)/t-1, csc t (1-t cot t))`

Explanation:

f(t) = ( x(t), y(t0).
f'(t) = ( x'(t), y'(t)).

x(t) = `(ln t )^2-t = u^2 -t, u=ln t`..
Applying function of function rule, f'(t)=2uu'(t)-1= `2( ln t)/t-1`.

y(t) = t csc t.
Applying product rule,
y'(t) = `csct-t csc t cot t=csc t (1-t cot t)`.#