Log Rule for Derivatives

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How the derivative rule for logs can be derived numerically.

How the derivative rule for logs can be derived numerically.

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