So, I think there is a bug here: when one applies the differentiation operator D to something which has the head of Piecewise it shouldn't differentiate the expression for each condition independently, because the value of a derivative of a function at some point depends not only on the value of the function at that point, but also on all the values of the function in the infinitesimal neighbourhood of that point. WolframAlpha brings expert-level knowledge and capabilities to the broadest possible range of peoplespanning all professions and education levels. Now, if we try to calculate the value of its derivative at x=0, then Mathematica assumes that it depends only on the value of y at x=0: y'īut of course this is not true - this function is not differentiable at x=0, because for x!=0 we have: y' = Sin - Cos/xĪnd the above expression has no limit as x approaches 0 and Mathematica knows this very well: Limit - Cos/x, x -> 0]Īlso, just taking the definition of derivative (as a limit) at x=0 we would end up with Limit,h->0] which of course doesn't exist. Using the "default value" syntax of Piecewise one can define the function equal to x*sin(1/x) for non-zero x and equal to 0 for x=0 in the following compact form: y := Piecewise ![]() Finance, Statistics & Business Analysis Logarithmic Derivative - from Wolfram MathWorld Calculus and Analysis Calculus Differential Calculus Calculus and Analysis Special Functions Logarithms Logarithmic Derivative The logarithmic derivative of a function is defined as the derivative of the logarithm of a function.Wolfram Knowledgebase Curated computable knowledge powering Wolfram|Alpha. Wolfram Universal Deployment System Instant deployment across cloud, desktop, mobile, and more. ![]() An Introduction to the Fractional Calculus and Fractional Differential Equations. Fractional Calculus, Fractional Integral Equation, Riemann-Liouville Operator, Semi-Integral Explore with WolframAlpha More things to try: References Miller, K. Tutorial for Mathematica & Wolfram Language. The study of fractional derivatives and integrals is called fractional calculus. ![]() Keep results symbolic or get a numerical approximation. This widget will let you get the directional derivative of any function. Wolfram Language & System Documentation Center BUILT-IN SYMBOL Constant Constant Constant is an attribute that indicates zero derivative of a symbol with respect to all parameters. Wolfram Data Framework Semantic framework for real-world data. How to calculate partial derivatives and multiple integrals for calculus.
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