Derivatives of Log Functions

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Presentation transcript:

Derivatives of Log Functions Lesson 4.5

Problem Consider f(x) = logax What if we try to use the definition for derivative using the limit No way to break up this portion of the expression to let h → 0

Possible Solution We know that the derivative is the "slope function" What if we graph y=ln(x) and check the slopes … plotting them

Slope Results The table at the right shows the values of the slopes at various x values What function might this be? Appears to be x slope of ln(x) at x 0.001 1000.000 0.010 100.000 0.100 10.000 0.500 2.000 0.750 1.333 1.000 1.500 0.667 5.000 0.200

Derivative of the Log Function For the natural logarithm ln(x) For the log of a different base loga(x)

Examples Try these sample problems … find the derivative Don't forget to use the chain rule where applicable

What About ln(-x)? Consider it a compound function Apply the chain rule Thus we see

Conclusion We now can say Apply to finding these derivatives

Assignment Lesson 4.5 Page 289 Exercises 1 – 65 EOO