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How the derivative rule for logs can be derived numerically.

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- 1. The Derivative of ln(x)<br />Numerically estimate the derivative at the following input values.<br />
- 2. Let’s see how this looks for x = 10.<br />
- 3. Let’s see how this looks for x = 10.<br />
- 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. 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. 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. 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. 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. The Derivative of ln(x)<br />Numerically estimate the derivative at the following input values.<br />
- 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. The Derivative of ln(x)<br />Numerically estimate the derivative at the following input values.<br />
- 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. The Derivative of ln(x)<br />If y = ln(x), then for x > 0.<br />

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