What is the derivative of $f (t) = (t - ln t, t^{2} sin t)$ $f(t) = (t-lnt, t^2sint )$ ?

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Answer 1 · 2016-01-10T12:47:10

$f'(t)=(y'(t))/(x'(t))$

$x'(t)=1-1/t = (t-1)/t$

$y'(t) = 2tsint+t^2cost$

$f'(t) = (2tsint+t^2cost)/((t-1)/t)$

$f'(t) = (t^2(2sint+tcost))/(t-1)$

What is the derivative of f(t) = (t-lnt, t^2sint ) f(t)=(t−lnt,t2sint)f(t) = (t-lnt, t^2sint ) ?