About: Rules of derivation   Sponge Permalink

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Requires: Derivative, Limits of functions, Newton's binomial - Derivative of the function "integer power", using Newton's binomial. therefore, if , - Derivative of the sum, substraction and multiplication times a number: "linearity"... by now we only can do polynomials!! - What about product of functions? Leibniz Rule, let's check whether it works with two monomials - What happens when the power is not an integer? Case of the square root or 1/x... we accept by now the extension of the rule... - Exponential function, special value of "e" - And the logarithm? Let's check the inverse function...

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  • Rules of derivation
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  • Requires: Derivative, Limits of functions, Newton's binomial - Derivative of the function "integer power", using Newton's binomial. therefore, if , - Derivative of the sum, substraction and multiplication times a number: "linearity"... by now we only can do polynomials!! - What about product of functions? Leibniz Rule, let's check whether it works with two monomials - What happens when the power is not an integer? Case of the square root or 1/x... we accept by now the extension of the rule... - Exponential function, special value of "e" - And the logarithm? Let's check the inverse function...
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abstract
  • Requires: Derivative, Limits of functions, Newton's binomial - Derivative of the function "integer power", using Newton's binomial. therefore, if , - Derivative of the sum, substraction and multiplication times a number: "linearity"... by now we only can do polynomials!! - What about product of functions? Leibniz Rule, let's check whether it works with two monomials - What happens when the power is not an integer? Case of the square root or 1/x... we accept by now the extension of the rule... - Exponential function, special value of "e" - And the logarithm? Let's check the inverse function... - And the compound function? Chain rule, What does it really mean? Let's check a simple example: - Now, with exp and log, let's return to the power of real exponent OK! It's coherent!! - Go on with trigonometric functions starting with when , - Summary of rules and applications Now read: Integration, Taylor series, 1D Optimizacin New terms: Leibniz rule, Chain rule
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