y=|x|(tanx)^(1/2)

find y'

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- Feb 10th 2010, 08:41 PMNoxideDerivative
y=|x|(tanx)^(1/2)

find y' - Feb 10th 2010, 09:03 PMGeneral
- Feb 10th 2010, 09:24 PMlgstarn
Run the online derivative calculator:

webMathematica Explorations: Step-by-Step Derivatives

Derivative of: x*Tan[x]^(1/2)

With respect to: x

Gives:

This is valid for

For , you have

Derivative of: -x*Tan[x]^(1/2)

With respect to: x

which gives:

So we can combine these two into one expression for :

- Feb 11th 2010, 09:15 AMNoxide
thanks, i was on the right track

- Feb 11th 2010, 10:17 AMNoxide
is it correct to say (with respect to my first question):

if x = 0 then y = 0 and d0/dx = 0?

or should i differentiate first using the positive case of x then input the value of x into the derivative and get 0? - Feb 12th 2010, 07:49 AMlgstarn
Well, if is a function of , in other words, , you can't do that directly. In this case,

So we compute the derivative as before to find . Only once you've done that can you put in to find what the value of is.

But because you have an absolute value, at the derivative doesn't exist. That's because the slope of the tangent line of changes sign at . - Feb 13th 2010, 12:11 PMNoxide
Thanks.

I can picture that there would be an infinite number of tangent lines at that point. So there are infinite derivatives. Is there a way to get a general equation for those infinite derivatives? - Feb 13th 2010, 12:44 PMdrumist
We just say it isn't differentiable at x=0 and exclude the point x=0 from the domain of the derivative. You don't need to bother doing anything else.

The domains of the function and its derivative are a bit complicated though (since only exists where ). Are you asked to state the domain of the derivative? - Feb 13th 2010, 01:06 PMlgstarn
Actually, you are correct! That is the concept of a "weak derivative." This is a bit advanced though. You wouldn't have to see that stuff until you became a graduate student or a senior working in mathematics.

Don't let the following links blow your mind - just be aware that what you are talking about does exist.

Weak derivative - Wikipedia, the free encyclopedia

Subderivative - Wikipedia, the free encyclopedia