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How do you differentiate #g(t) = sqrt (t) + 4sec(t)#?

Answer 1

Charles Anctil

Use the sum rule and the derivatives of #sqrtt# and #sect#.

The derivative os a sum is the sum of the derivatives, so we differentiate term by term.

The first term #sqrtt# has derivative #1/(2sqrtt)# (Use the power rule)

The second term #sect# has derivative #sect tant#

So #g'(t) = 1/(2sqrtt) +sect tant#

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Answer 2

Axel Alvarez

To differentiate ( g(t) = \sqrt{t} + 4\sec(t) ), we use the sum rule and the chain rule. The derivative is:

[ g'(t) = \frac{1}{2\sqrt{t}} + 4\sec(t)\tan(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.