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3.3 Differentiation Rules for Exponentials and Logarithms

Differentiation Rules for Exponentials and Logarithms

• The other rules regarding differentiation such as addition, subtraction, multiplication, division of functions, chain rule etc. applies too.
• All of these rules can be proven via first principles, but it is not required.
• The basic rules in this section are:

i) If f(x)=a^{x}, \text { then } f^{\prime}(x)=a^{x} \ln a

ii) If f(x)=\log _{a} x, \text { then } f^{\prime}(x)=\frac{1}{x}(\ln a)^{-1}

where n \neq 0, n \in R (or n \in R \backslash\{0\})

• Applying the rules to natural exponential and logarithm functions (i.e. a=e), yields:
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