query: Proving Derivative at 0 exists
positive_passages.docid: 1371
positive_passages.text: Prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$.
negative_passages.docid: 112898
negative_passages.text: Derivative of sin(x)/x at $0$ by definition of derivative
negative_passages.docid: 16375
negative_passages.text: Is the function differentiable at $0$?
negative_passages.docid: 147299
negative_passages.text: Prove that $g(x,y) = \frac{x^3y}{x^2+y^2}$ with $g(0,0)=0$ is continuous
negative_passages.docid: 61640
negative_passages.text: Prove c exists for f:[0,1] -> R
negative_passages.docid: 150833
negative_passages.text: Discontinuities of the derivative of a differentiable function on closed interval
negative_passages.docid: 62352
negative_passages.text: Proving a scalar function is differentiable at the origin but that its partial derivatives are not continuous at that point.
negative_passages.docid: 107290
negative_passages.text: proof of product rule of derivatives using first principle?
negative_passages.docid: 11167
negative_passages.text: A counterexample of a differentiable function on an interval whose derivative is discontinuous
negative_passages.docid: 40549
negative_passages.text: How to proof the the derivative of $x^2$ is $2x$?
negative_passages.docid: 3387
negative_passages.text: Derivative of $f(x)=|x|$
negative_passages.docid: 13656
negative_passages.text: Prove existence of a real root.
negative_passages.docid: 124499
negative_passages.text: Where is the error in my proof that all derivatives are continuous?
negative_passages.docid: 82001
negative_passages.text: How to prove the function is a constant
negative_passages.docid: 117338
negative_passages.text: Counterexample to second derivative test when f''(x) is not continuously differentiable
negative_passages.docid: 34187
negative_passages.text: The limit of the derivative of an increasing and bounded function is always $0$?
negative_passages.docid: 113343
negative_passages.text: $f$ is constant if derivative equals zero