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10. Derivatives of Log Functions

10. Derivatives of Log Functions. Some reminders about log functions. They have a vertical asymptote They have unique properties Ln is log base e. Example 1 – solve the following equations. Example 2. Find dy /dx of y = ln x using implicit differentiation. Derivative of ln. Example 3.

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10. Derivatives of Log Functions

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  1. 10. Derivatives of Log Functions

  2. Some reminders about log functions • They have a vertical asymptote • They have unique properties • Ln is log base e

  3. Example 1 – solve the following equations

  4. Example 2 Find dy/dx of y = ln x using implicit differentiation

  5. Derivative of ln

  6. Example 3 Find the derivative of each

  7. Example 4 Find dy/dx of y = logb x using the change of base formula (logba = log a/log b)

  8. Derivative of log

  9. Example 5 Find the derivative of

  10. Logarithmic Differentiation (LOG DIFF) • This technique involves taking the natural log of BOTH sides of an equation prior to differentiating. We can use this technique in 3 situations • We are differentiating an “ugly” expression with logs of factors in a product or a quotient • When we are differentiating a function of the form y = f(x)g(x) • When the instructions tell you to

  11. Example 6 - Use LOG DIFF to find dy/dx

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