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

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Answer 1 · 2017-11-24T07:17:48

$(dy)/(dx)=(2t-sect-tsect tant)/(cos^2t-tsin2t)$

When a functiion is given in parametric form such as $f(t)=(x(t),y(t))$ , its dervative is given by $(dy)/(dx)=((dy)/(dt))/((dx)/(dt))$

Here we have $y(t)=t^2-tsect$ hence $(dy)/(dt)=2t-sect-tsect tant$

and $x(t)=tcos^2t$ hence $(dx)/(dt)=cos^2t+txx2costxx(-sint)$

= $cos^2t-tsin2t$

Hence $(dy)/(dx)=(2t-sect-tsect tant)/(cos^2t-tsin2t)$

What is the derivative of f(t) = (tcos^2t , t^2-t sect ) f(t) = (tcos^2t , t^2-t sect ) ?