# analysis - Derivative of a sequence - Mathematics Stack.

3 Answers. The derivative of f at c (for c finite) is defined as the following limit (if it exists): f′(c)=lim x→cf(x)−f(c) x−c. By limx→c we mean that we need to be able to take x as close as we want to c in order for this to even make sense. The issue with your sequence an=1 n2 is that an is technically speaking. ## When limit of derivative of uniformly convergent sequence.

We know, we can't claim much about convergence of derivative \$\f'_n(x)\\$, and it may not even be pointwise convergent. All the counter-examples I have seen till date, appear to have either non-differentiable sequence of functions or pointwise divergent derivatives or non differentiable limit function.

### real analysis - Limit of Sequence of Differentiable.

Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute, real-analysis functional-analysis limits analysis uniform-convergence, sharecite. Cauchy Sequence of Differentiable Functions Implies Cauchy Sequence of Derivatives? 0. calculus and analysis - Using partial derivatives in. Traditional mathematical notation is far from unambiguous. \$\endgroup\$ – Szabolcs Dec 7 '17 at 10:07 \$\begingroup\$ But if you really want to, you can type the following sequence of keys: ESC pd ESC Ctrl-_.real analysis - derivatives and uniformly convergence. Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Visit Stack.Real Analysis: Derivatives and Sequences - BrainMass Show that the equation f(x) = 0 has a unique root in [a,b]. Show also that for any given x1 &1108; [a,b], the sequence (xn), xn1 = xn - for n = 1, 2. is well defined (i, e, for each n, xn &1108; [a,b]), and that xn &61664; as n &61664; &8734; where &1108; [a,b] is such that f( ) =0. See attached file for full problem description.real analysis - Limit of Sequence of Differentiable. Question Idea network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share.mathematical analysis - Problem with derivative of sigmoid. Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of computer science. Problem with derivative of sigmoid activation function. Ask Question 0. Browse other questions tagged mathematical-analysis or ask your own question, asked. 4 years, 11 months ago, viewed. 319 times.

Analysismathematics

Analysis: Analysis, a branch of mathematics that deals with continuous change and with certain general types of processes that have emerged from the study of continuous change, such as limits, differentiation, and integration. Since the discovery of the differential and integral calculus by.

WolframAlpha Examples: Derivatives

WolframAlpha is a great resource for determining the differentiability of a function, as well as calculating the derivatives of trigonometric, logarithmic, exponential, polynomial and many other types of mathematical expressions. Differentiation has many applications within physics, trigonometry, analysis, optimization and other fields.