Question

How do you find the derivative of `sqrt(cosx)`?

Answer 1

The answer is `−sin(x)/(2sqrt(cos(x))`

Explanation:

This problem is not all that difficult; you just need to rearrange it to make it easier. First thing I would do is re-write it as:

`(cos(x))^(1/2)`.

This makes it easier to look at things, and to apply our rules. Applying the chain rule now leaves us with the following:

`((1/2)(cosx)^(-1/2)) * (-sinx)`

Note: The negative sine of x comes as a result of your rule for cosine; you should have this memorised if you don't already

Now, just go ahead and put together the terms:

`(-sinx(cosx)^(-1/2))/2`

Depending on your requirements, you can either leave it as is, or simplify further to get the final answer:

`−sin(x)/(2sqrt(cos(x))`

Hope that helped :)