# How do you find the derivative of #x = tan (x+y)#?

Method II

Method III

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To find the derivative of ( x = \tan(x + y) ) with respect to ( x ), we use the chain rule, which states that the derivative of a composition of functions is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

Differentiating ( \tan(x + y) ) with respect to ( x ), we get:

[ \frac{d}{dx} \tan(x + y) = \sec^2(x + y) \cdot (1 + \frac{d}{dx}(x + y)) ]

[ = \sec^2(x + y) \cdot (1 + 1) ]

[ = \sec^2(x + y) \cdot 2 ]

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

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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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