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# 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 &gt; 0.