query: Clarification on the definition of derivative/differentiablility
positive_passages.docid: 151109
positive_passages.text: Verification that $\lim_{x \to a}\frac{f(x)-f(a)}{x-a}$ and $\lim_{h\to 0}\frac{f(a+h) -f(a)}{h}$ are equivalent definitions of the derivative.
negative_passages.docid: 114691
negative_passages.text: Why can't differentiability be generalized as nicely as continuity?
negative_passages.docid: 77624
negative_passages.text: Characterization of sets of differentiability
negative_passages.docid: 31685
negative_passages.text: Differentiability of $f(x) = x^2 \sin{\frac{1}{x}}$ and $f'$
negative_passages.docid: 16291
negative_passages.text: Discontinuous derivative.
negative_passages.docid: 13150
negative_passages.text: If the derivative of $f$ is never zero, then $f$ is one-to-one
negative_passages.docid: 40429
negative_passages.text: Differentiability of this picewise function
negative_passages.docid: 1246
negative_passages.text: Differences between derivatives and strong derivatives
negative_passages.docid: 89057
negative_passages.text: How does one properly define the derivative of one operator-valued function?
negative_passages.docid: 76589
negative_passages.text: When does product of derivatives equals derivative of products?
negative_passages.docid: 23975
negative_passages.text: What is the practical difference between a differential and a derivative?
negative_passages.docid: 131357
negative_passages.text: Prove that $f(x,y)=xy$ is differentiable using the definition
negative_passages.docid: 101037
negative_passages.text: The given limit is a derivative, but of what function and at what point?
negative_passages.docid: 105767
negative_passages.text: derivative under integral intuition
negative_passages.docid: 48980
negative_passages.text: Geometrical Meaning of derivative of complex function
negative_passages.docid: 23510
negative_passages.text: different possible definitions of the exterior derivative?
negative_passages.docid: 156536
negative_passages.text: Defining functions as derivatives