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

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Answer 1 · 2015-09-20T08:21:24

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

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 :)