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Derivative of Exponential Function and Logarithms

Dive into exponential functions and logarithmic derivatives with bases other than e. Learn the change of base rule, logarithmic differentiation, and handling variables in bases and powers. Examples included!

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Derivative of Exponential Function and Logarithms

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  1. Derivative of Exponential Function and Logarithms I Logarithms, still 

  2. Now, when e is missing Instead of exponential function with base e (which is a number) we will look at exponential functions with bases other than e. As well, we’ll also look at the logarithmic function when base ≠ e. How fun!

  3. Onto the derivatives Change of base rule

  4. Another Derivative (easier)

  5. Logarithmic Differentiation What do we do when both the base AND the powers have variables? Hmmm.. Lets see…. Power rule? The exponential rule? I’m so confused!! Hint: take the ln of both sides!! 

  6. Examples Find dy/dx for the following:

  7. Examples Find dy/dx for the following:

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