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

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Answer 1 · 2016-03-25T10:03:06

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

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) = $csct-t csc t cot t=csc t (1-t cot t)$ .#

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