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How do you differentiate # g(x) =sec^2 x + tan^2 x #?

Answer 1

#d/(d x)g(x)=4 tan x sec^2 x#

#d/(d x)g(x)=2 sec x tan x sec x+2 tan x sec^2x# #d/(d x)g(x)=2tan x sec^2 x+2 tan x sec^2 x# #d/(d x)g(x)=4 tan x sec^2 x#

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Answer 2

Paisley Johnson

To differentiate g(x) = sec^2(x) + tan^2(x), use the following steps:

Differentiate sec^2(x) with respect to x.
Differentiate tan^2(x) with respect to x.
Add the results from steps 1 and 2.

Here's the breakdown:

The derivative of sec^2(x) is 2 * sec(x) * tan(x) * sec(x).
The derivative of tan^2(x) is 2 * tan(x) * sec^2(x).
Adding the results from steps 1 and 2, we get the derivative of g(x) as 2 * sec(x) * tan(x) * sec(x) + 2 * tan(x) * sec^2(x).

Simplify the expression if necessary, but this is the derivative of g(x).

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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.