# How do you find the derivative of Inverse trig function #y = cos sec^2(x)#?

As typed, there is no inverse trig function here.

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To find the derivative of the inverse trigonometric function ( y = \cos(\sec^2(x)) ), we'll need to use the chain rule and the derivative formulas for inverse trig functions.

The chain rule states that if we have a function of a function, we differentiate the outer function first and then multiply by the derivative of the inner function.

The derivative of ( \cos(u) ) is ( -\sin(u) ), and the derivative of ( \sec^2(x) ) is ( 2\sec(x)\tan(x) ).

Applying the chain rule:

[ \frac{dy}{dx} = -\sin(\sec^2(x)) \times 2\sec(x)\tan(x) ]

This can be simplified as:

[ \frac{dy}{dx} = -2\sec(x)\tan(x)\sin(\sec^2(x)) ]

So, the derivative of ( y = \cos(\sec^2(x)) ) with respect to ( x ) is ( -2\sec(x)\tan(x)\sin(\sec^2(x)) ).

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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.

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.

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.

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