SOLUTION: Find the deivative using the increment steps. 1. Y = (x^2 - 7)/(x^2 + 3)

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Question 1131246: Find the deivative using the increment steps.
1. Y = (x^2 - 7)/(x^2 + 3)
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


We COULD do this:

limit as h goes to 0 of (1/h)* %28%28x%2Bh%29%5E2-7%29%2F%28%28x%2Bh%29%5E2%2B3%29-%28x%5E2-7%29%2F%28x%5E2%2B3%29.

But finding the derivative is going to be somewhat less work if we rewrite the function as

f%28x%29+=+1-10%2F%28x%5E2%2B3%29

Then to find the derivative using increment steps, we do

limit as h goes to 0 of (1/h)*%28%281-10%2F%28%28x%2Bh%29%5E2%2B3%29%29-%281-10%2F%28x%5E2%2B3%29%29%29



Then 1/h* 10%28%282xh%2Bh%5E2%29%2F%28%28x%5E2%2B3%29%28%28x%2Bh%29%5E2%2B3%29%29%29 = 10%28%282x%2Bh%29%2F%28%28x%5E2%2B3%29%28%28x%2Bh%29%5E2%2B3%29%29%29

And finally

limit as h goes to 0 of 10%28%282x%2Bh%29%2F%28%28x%5E2%2B3%29%28%28x%2Bh%29%5E2%2B3%29%29%29 = 20x%2F%28x%5E2%2B3%29%5E2