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# C1 Differentiation Watch

1. Hi,
can you help me how to differentiate roots?

Look at this one:

Spoiler:
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€: I know how to do the dy/dx part, but I don't understand how they've changed the root into the fractional form :?
2. You should remember that anything to the power of a half means you square root it. So , for example. Also remember that anything to the power of -1 is "one over" that number. So .

Then you can put the two rules together if needed. For example,

Is that now clear?

y = 1/4x^-1/2

dy/dx = (1/4 * -1/2) * x ^ (-1/2 -1)

Bring the power down and multiply it

After bring down the power, we need to minus it by 1

dy/dx = -1/8x^-3/2
4. (Original post by StylaBoy)
Hi,
can you help me how to differentiate roots?

Look at this one:

Spoiler:
Show

€: I know how to do the dy/dx part, but I don't understand how they've changed the root into the fractional form :?
You should know the following base identities

where x>0 and
5. 1 over can be turned into 1/4 of x to the negative 1/2 because that fraction can be split up into two parts: one over the square root of x multiplied by one over 4. By now you should know that the square root of x equals x to the power 1/2, and one over the square root of anything equals that to the negative 1/2). This is very basic stuff.

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Updated: November 30, 2010
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