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

Answer 1

Isabella Ackerman

#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#

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Answer 2

Charles Anctil

To differentiate g(t) = 4sec(t) + tan(t), you would apply the rules of differentiation to each term separately. The derivative of sec(t) is sec(t)tan(t), and the derivative of tan(t) is sec^2(t). Therefore, the derivative of g(t) with respect to t is:

g'(t) = 4(sec(t)tan(t)) + sec^2(t)

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.