Logarithmic and exponential differentiation rules

The derivative rules for logarithmic and exponential functions are as follows:
  • `d/{dx}ln(x) = 1/x`
  • `d/{dx}e^x = e^x`
The above rules are however only for natural logarithmic functions (logarithms having base e) and exopnential functions having base e. When the base of a logarithm is any number, say 'a' other than e, then its derivative is given by:
`d/{dx} log_a(x) = 1/{x ln(a)}`
The derivative of an exponential function in which the base is a number other than 'e' is given by
`d/{dx} a^x = a^x ln(a)` . . . where 'a' is any number number

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