The Derivative of Log Functions

1
The Derivative of Log Functions

• To find the derivative of the function ylogx we
  need to go back to limits.

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Log Derivatives

• If f(x)log x then

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Log Derivatives

• Simplifying using the laws of logs

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Log Derivatives
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Log and Exponent Derivatives

• So we have the following rules
• The derivative of logx is 1/x loge
• The derivative of lnx is 1/x lne
• The derivative of ex is
• The derivative of 2x is
• The derivative of ax is

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Examples

• Find f '(x) if
• f(x)log(3x²5)
• f(x)ln(x5)
• f(x)5x²logx
• f(x)e2x5