The Derivative of ln(x)<br />Numerically estimate the derivative at the following input values.<br />
Let’s see how this looks for x = 10.<br />
Let’s see how this looks for x = 10.<br />
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 ...
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 ...
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 ...
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 ...
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 ...
The Derivative of ln(x)<br />Numerically estimate the derivative at the following input values.<br />
Now do the same thing to estimate the derivatives for the other functions.<br />The Derivative of ln(x)<br />Numerically e...
The Derivative of ln(x)<br />Numerically estimate the derivative at the following input values.<br />
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 />Num...
The Derivative of ln(x)<br />If y = ln(x), then              for x &gt; 0.<br />
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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 />

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