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I'm going to find the derivative by taking limit as H approaches
zero 1 / sqrt 11 minus Theta plus H - 1 / sqrt 11 minus Theta
all over H Getting a common denominator and then multiplying
by the conjugate simplifies up to the limit as H goes to 0.
If we just do our plugging and chugging, we get one over sqrt
11 minus Theta minus H * sqrt 11 minus Theta times the quantity
sqrt 11 minus Theta plus sqrt 11 minus Theta minus H If we stick
as H goes into zero, it simplifies up into this over
here.
So we have one of them times another of them times the
quantity of one plus one of those items.
So we have two of those items.
So we have two of sqrt 11 minus Theta three times the square
root we could really think of as the 1/2 power.
So 211 minus thetas to the three halves.
And it specifies that we want to know the slope or the derivative
at Theta equal 2.
So we're literally going to stick to and for Theta 1 / 2
times the quantity 11 -.
2 to the three halves.
11 -, 2 is 9 square root.
That two or that's two in the denominator means square root.
So sqrt 9 is 3/3 cubes 27, so 1 / 54.