+128407 sqrt [( x + h)^2 + 9 ] - sqrt [ x^2 + 9]
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h
sqrt [ x^2 + 2xh + h^2 + 9 ] - sqrt [ x^2 + 9]
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h
Multiply top / bottom by sqrt [ x^2 + 2xh + h^2 + 9 ] + sqrt [ x^2 + 9 ]
x^2 + 2xh + h^2 + 9 - x^2 - 9
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h [ ( sqrt x^2 + 2xh + h^2 + 9) + (sqrt (x^2 + 9) ]
2xh + h^2
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h [ ( sqrt x^2 + 2xh + h^2 + 9) + (sqrt (x^2 + 9) ]
h (2x + h)
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h [ ( sqrt x^2 + 2xh + h^2 + 9) + (sqrt (x^2 + 9) ]
2x + h
______________________________________ let h approach 0 and we have
[ ( sqrt x^2 + 2xh + h^2 + 9) + (sqrt (x^2 + 9) ]
2x
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sqrt (x^2 + 9) + sqrt (x ^2 + 9)
2x
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2sqrt (x^2 + 9)
x
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sqrt (x^2 + 9)
If you take Calculus.....you will learn that the derivative of (x^2 + 9)^(1/2) =
(1/2) (2x) / ( (x^2 + 9)^(1/2) = x / sqrt ( x^2 + 9) = our result !!!!
