# What is the derivative of #(sinx + cosx) / (sinx - cosx)#?

Start by taking a look at your function

This means that you can differentiate this function by using the quotient rule, which allows you to find the derivative of a function that's the quotient of two other functions by using the formula

You also need to remember that

and that

I'll break this into two fractions to make the calculations easier to read

The first fraction will be equal to

You can further simplify this by using the fact that

The second fraction will be equal to

You can simplify this by using

to get

Put the two fractions back together to get

Finally, you get

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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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