Rules of differentiation: Conclusion of rules of differentiation
Summary
Thanks to this chapter you can differentiate functions resulting from operations (like addition, subtraction, multiplication, division, composition, and inversion) on differentiable functions. This is based on the following calculation rules.
| Name | function | derivative |
| Extended sum rule | #a\cdot f(x)+b\cdot g(x)# | #a \cdot f'(x)+b\cdot g'(x)# |
| Product rule | #f(x)\cdot g(x)# | #f'(x)\cdot g(x)+f(x) \cdot g'(x)# |
| Quotient Rule | #\frac{f(x)}{g(x)}# | #\frac{f'(x)\cdot g(x)-f(x)\cdot g'(x)}{(g(x))^2}# |
| Chain-rule | #f(g(x))# | #f'(g(x)) \cdot g'(x)# |
| Inverse function rule | #f^{-1}(x)# | #\left({f}^{-1}\right)'(x) = \dfrac{1}{f'\left(f^{-1}(x)\right)}# |
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