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Derivative using first principle method

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#derivatives
135
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Function with bounded $f''$ on $(0,\infty)$ and $f(x) \to 0$ as $ x\to \infty$ then $f'(x) \to 0$ as $ x\to \infty$

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#real-analysis #analysis #derivatives #uniform-continuity
77
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Derivative of $f(x) = \frac{x^3+\cos x}{6}$

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#calculus #derivatives
387
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Bounded derivative of increasing function

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#calculus #functions #derivatives
46
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Fréchet space of Hölder continuous differentiable functions

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#general-topology #derivatives #holder-spaces
93
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Unclear calculus problem

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#calculus #integration #algebra-precalculus #derivatives #indefinite-integrals
17
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Interpretation of changing the inputs of the partial differentation of a function

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#calculus #multivariable-calculus #functions #derivatives #partial-derivative
75
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Prove that $m(y − x) ≤ f(y) − f(x) ≤ M(y − x)$

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#derivatives #continuity
550
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Theorem 5.16 in Apostol's MATHEMATICAL ANALYSIS, 2nd ed: Intermediate-Value Theorem for Derivatives

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#calculus #real-analysis #analysis #derivatives #proof-explanation
1.4k
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Connecting smooth functions in a smooth way

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#calculus #derivatives #smooth-functions
911
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derivative of the determinant of the sum of two matrices

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#matrices #derivatives #matrix-calculus #trace
20.6k
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Derivative of Euclidean norm (L2 norm)

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#derivatives #normed-spaces
50
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Chain rule verification

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#calculus #matrices #derivatives #partial-derivative #chain-rule
73
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Validation of $\frac{\partial \mathcal{R} (\mathbf{x})}{\partial \mathbf{x}^T}$

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#linear-algebra #derivatives #matrix-calculus
258
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An example of a function that is analytic only on the upper-half plane

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#complex-analysis #derivatives

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