How do you differentiate $g(t)=4sect+tant$ ?

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Answer 1 · 2017-05-02T22:44:01

$g'(t)=4sect tant+sec^2t=sect(4tant+sect)$

The following trigonometric derivatives are very useful:

Thus,

$g'(t)=4sect tant+sec^2t=sect(4tant+sect)$

We can derive both of these derivatives:

$sect=(cost)^-1$

$d/dxsect=-(cost)^-2d/dtcost=(-1)/cos^2t(-sint)$

$=sect tant$

And:

$tant=sint/cost$

$d/dttant=((d/dtsint)cost-sint(d/dtcost))/cos^2t=(cos^2t+sin^2t)/cos^2t$

$=sec^2t$

How do you differentiate g(t)=4sect+tantg(t)=4sect+tant?