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

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To differentiate y = sec^2(x) + tan^2(x), you can use the chain rule and the derivatives of sec^2(x) and tan^2(x). The derivative of sec^2(x) is 2sec(x)tan(x)sec(x), and the derivative of tan^2(x) is 2tan(x)sec^2(x). Therefore, the derivative of y with respect to x is:

dy/dx = d/dx(sec^2(x)) + d/dx(tan^2(x)) dy/dx = 2sec(x)tan(x)sec(x) + 2tan(x)sec^2(x) dy/dx = 2sec^2(x)tan(x) + 2tan(x)sec^2(x) dy/dx = 2sec^2(x)tan(x) + 2tan(x)sec^2(x)

So, the derivative of y = sec^2(x) + tan^2(x) is dy/dx = 2sec^2(x)tan(x) + 2tan(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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