# How do you differentiate #y=4/cosx#?

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To differentiate ( y = \frac{4}{\cos(x)} ), you can use the quotient rule. The quotient rule states that for a function ( y = \frac{u}{v} ), where ( u ) and ( v ) are functions of ( x ), the derivative ( \frac{dy}{dx} ) is given by:

[ \frac{dy}{dx} = \frac{v \cdot \frac{du}{dx} - u \cdot \frac{dv}{dx}}{v^2} ]

For ( y = \frac{4}{\cos(x)} ), ( u = 4 ) and ( v = \cos(x) ). Now, differentiate ( u ) and ( v ) with respect to ( x ):

[ \frac{du}{dx} = 0 ] [ \frac{dv}{dx} = -\sin(x) ]

Now, plug these values into the quotient rule formula:

[ \frac{dy}{dx} = \frac{\cos(x) \cdot 0 - 4 \cdot (-\sin(x))}{\cos^2(x)} ] [ \frac{dy}{dx} = \frac{4\sin(x)}{\cos^2(x)} ] [ \frac{dy}{dx} = 4\sin(x)\sec^2(x) ]

So, the derivative of ( y = \frac{4}{\cos(x)} ) with respect to ( x ) is ( 4\sin(x)\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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