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# Log Rule for Derivatives

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How the derivative rule for logs can be derived numerically.

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### Log Rule for Derivatives

1. 1. The Derivative of ln(x)<br />Numerically estimate the derivative at the following input values.<br />
2. 2. Let’s see how this looks for x = 10.<br />
3. 3. Let’s see how this looks for x = 10.<br />
4. 4. Let’s see how this looks for x = 10.<br />Now there’s not much simplification we can do here so let’s see what happens as h gets closer to 0<br />
5. 5. Let’s see how this looks for x = 10.<br />Now there’s not much simplification we can do here so let’s see what happens as h gets closer to 0<br />
6. 6. Let’s see how this looks for x = 10.<br />Now there’s not much simplification we can do here so let’s see what happens as h gets closer to 0<br />
7. 7. Let’s see how this looks for x = 10.<br />Now there’s not much simplification we can do here so let’s see what happens as h gets closer to 0<br />
8. 8. Let’s see how this looks for x = 10.<br />Now there’s not much simplification we can do here so let’s see what happens as h gets closer to 0<br />So it converges to 0.1<br />
9. 9. The Derivative of ln(x)<br />Numerically estimate the derivative at the following input values.<br />
10. 10. Now do the same thing to estimate the derivatives for the other functions.<br />The Derivative of ln(x)<br />Numerically estimate the derivative at the following input values.<br />
11. 11. The Derivative of ln(x)<br />Numerically estimate the derivative at the following input values.<br />
12. 12. In each case the derivative is the reciprocal so we have our rule for f(x) = ln(x)<br />The Derivative of ln(x)<br />Numerically estimate the derivative at the following input values.<br />
13. 13. The Derivative of ln(x)<br />If y = ln(x), then for x &gt; 0.<br />