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MAT 213 Brief Calculus

Section 3.3 Exponential and Logarithmic Rate-of-Change Formulas. MAT 213 Brief Calculus. Below is a graph of f ( x ) =2 x What do you think the graph of f’ ( x ) would look like?. What is this????. The Derivatives of Exponential Functions Calculate the derivative of f ( x ) =2 x.

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MAT 213 Brief Calculus

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  1. Section 3.3 Exponential and Logarithmic Rate-of-Change Formulas MAT 213 Brief Calculus

  2. Below is a graph of f(x)=2x What do you think the graph of f’(x) would look like?

  3. What is this???? The Derivatives of Exponential Functions Calculate the derivative of f(x)=2x

  4. The Derivatives of Exponential Functions Fill out the following table for values of h close to zero.

  5. The Derivatives of Exponential Functions Fill out the following table for values of h close to zero. This table suggests that the limit DOES exist, and has a value of about 0.693 So we can write:

  6. So the derivative of 2x is proportional to 2xwith a constant of proportionality 0.693. Hmmmm…

  7. The Derivatives of Exponential Functions Calculate the derivative of f(x)=ax What is this????

  8. Use your calculator to plot these points. What type of function does it look like? Here is for different values of a

  9. RESULTS Consequently,

  10. EXAMPLES

  11. The Derivative of ln x Numerically estimate the derivative at the following input values.

  12. The Derivative of ln x Numerically estimate the derivative at the following input values.

  13. The Derivative of ln x If y = lnx, then for x > 0. Examples

  14. In groups let’s try the following from the book • 23

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