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irspow
2006-02-12 01:53:17

The first thing that you must realize is that this is a composition function.  That just means that there is a function nested within another function.  To find the derivative of a composition function you need to take two derivatives, multiplying the outer derivative by the inner derivative.

You have:

y = 3√(16 - x²)/4,   I am assuming that everything after the radical sign is within it here

It is not 3/4(√(16 - x²)....right?

The first thing that I would do is to get everything within the radical sign;

y = √[(144 - 9x²) / 4]

The derivative of √x is 1 / (2√x)

So the outer derivative is just;

1 / {2√[(144 - 9x²) / 4]}

The derivative of the inner function ( 144 - 9x²) / 4 is;

If you are not sure what the derivative of a fraction is, this is the formula;

if y = f(g)/f(h)

y' = [f'(g)f(h) - f(g)f'(h)] / f(h)²

Getting back to the problem at hand, ( 144 - 9x²) / 4 and using the formula above gives;

[-18x(4) - 0(144 - 9x²)] / 16 =  -9x / 2

Multiplying our outer derivative by our inner derivative gives;

1 / {2√[(144 - 9x²) / 4]}  ×  -9x / 2 = -x / [9√(16 - x²)]

I hope this helps...if you did not understand any of the steps just ask.

rp_
2006-02-12 01:01:27