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How do you find the derivative of #w^2 sec^2(3w)#?

Answer 1

William Abdalla

Its derivative can be found by this way

#2wsec^2(3w)+w^2. 2sec(3w)(sec3wtan3w)(3)#

#2wsec^2(3w)+6w^2sec^2(3w) tan3w#

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Answer 2

Evelyn Agard

To find the derivative of w^2 sec^2(3w), use the chain rule:

Differentiate the outer function, which is sec^2(3w), to get 2 * sec(3w) * tan(3w) * 3.
Multiply by the derivative of the inner function, which is 2w.

The result is:

dw/dw = 2w * 2 * sec(3w) * tan(3w) * 3 = 12w * sec(3w) * tan(3w)

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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.