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How do you find the derivative of #y=sec4x#?

Answer 1

Christopher Agresta

#y'=4sec x tan x#

In this example we will have to use the Chain Rule.

We have to take the derivative of the outside, #sec x#.

We also have to take the derivative of the inside, #4x#.

We then multiply those derivatives together.

#d/dx sec x = sec x tan x#

#d/dx 4x=4#

#y'=sec x tan x * 4#

#y'=4sec x tan x#

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Answer 2

Samantha Adkison

To find the derivative of (y = \sec(4x)), we can use the chain rule.

The derivative of (\sec(u)) with respect to (u) is (\sec(u) \tan(u)).

Let (u = 4x). Then, (\frac{du}{dx} = 4).

So, applying the chain rule, the derivative of (y) with respect to (x) is:

[ \frac{dy}{dx} = \sec(4x) \tan(4x) \times 4 ]

[ \frac{dy}{dx} = 4\sec(4x) \tan(4x) ]

Therefore, the derivative of (y = \sec(4x)) is (4\sec(4x) \tan(4x)).

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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.