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  • Understanding the derivative as a linear transformation
    29 It's been a while now I am studying multivariable calculus and the concept of differentiation in space (or higher dimension) I saw relative posts but one question remains I can't understand the concept of linear transformation that we use to define the Frechet derivative
  • calculus - Defining the derivative without limits - Mathematics Stack . . .
    0 Still another way to define the derivative without limits, in more constructive and finitist terms, is to re-cast the $ (\epsilon, \delta)$ definition in a purely algebraic form, somewhat reminiscent of nonstandard analysis and automatic differentiation
  • Proof of the derivative of $\ln (x)$ - Mathematics Stack Exchange
    Note, however, that this assumes that $\ln x$ is differentiable (That is required if you want to use the chain rule) So unless you have proved that $\ln x$ is differentiable, this proof cannot work As far as I can see, there is no better way to prove that $\ln x$ is differentiable that to calculate the derivative explicitly
  • What is the practical difference between a differential and a derivative?
    Also, notice an interesting reversal: originally, differentials came first, and they were used to define the derivative as a ratio Today, derivatives come first (defined as limits), and differentials are defined in terms of the derivatives What is the practical difference, though? You'll probably be disappointed to hear "not much"
  • multivariable calculus - What exactly is the difference between a . . .
    The difference between partial and total differentiation is that (total) differentiation claims that not only is $f$ locally linear, in a precise sense, w r t changes in one coordinate, but it is so in all coordinates, and I get a good picture of how $f$ behaves around a particular point when I totally differentiate
  • Why do we need a Lie derivative of a vector field?
    Since you can pull back tensors, it’s a lot easier to define and get a feel for what the Lie derivative of a tensor is than the Lie derivative of a vector field
  • What is $dx$ in integration? - Mathematics Stack Exchange
    Otherwise differentiation and integration would be impossible to understand in the context of algebra and geometry I strongly recommend Teach Yourself Calculus by P Abbott





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