Higher derivative
Builds on Derivative function
Definition
Let be an open interval and let . Let . If is defined and differentiable on , let , its derivative function. The function is the -th derivative of , and is times differentiable when it exists.
Remarks
The second derivative is .
For example, the -th derivative of is the constant .
Mathlib defines iteratedDeriv n f.
Reading path
To understand this page from the ground up, read these 6 pages in order. The foundations come first.
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- no evidence level
- Limit point of a set definition
- Limit of a function definition
- Derivative definition
- Differentiable function definition
- Derivative function definition
- Higher derivative definition
Where this leads
63 pages build on this one.
- Taylor's theorem with the Cauchy remainder
- 1 + x is at most exp x
- Reduction formula
- sin x / x tends to 1
- Taylor series
- Power series of sine
- Taylor's theorem with the Peano remainder
- Taylor's theorem
- Maclaurin series
- log x is at most x - 1
- Power series of the exponential function
- Continuously differentiable function
- Power series of cosine
- Integration by parts
- Smooth non-analytic function
- Smooth function
- Integration by substitution
- The exponential function is convex
- Trigonometric substitution
- The gamma function extends the factorial
- Second derivative test
- Dirichlet integral
- Taylor's theorem with the Lagrange remainder
- Taylor polynomial
- General Leibniz rule
- Stirling's formula
- pi is greater than 3
- Tangent half-angle substitution
- x^2 sin(1/x) is differentiable with discontinuous derivative
- Taylor's theorem with the integral remainder
- Wallis product
- Second derivative
- A function with nonnegative second derivative is convex
- Laplace's method
- Minimal curvature property of natural cubic splines
- Stein's unbiased risk estimate
- Cauchy–Pompeiu formula
- Bump function
- Stein's lemma
- Padé approximant
- Smoothing spline
- Peano kernel theorem
- Stein's example
- Quasi-analytic function
- Quadratic convergence of Newton's method
- Analytic function between Banach spaces
- Landau–Kolmogorov inequality
- Ramanujan summation
- Smoothness classes
- Regular surface
- Markov brothers' inequality
- Euler–Boole summation
- Wirtinger's inequality for functions
- Wiman–Valiron theory
- Padé table
- Differentiable dependence on parameters
- Denjoy–Carleman theorem
- Borel's lemma
- Error bound for the trapezoidal rule
- Finite difference coefficients
- Heun's method
- Abel's summation formula
- Midpoint method
Further reading
- Web https://en.wikipedia.org/wiki/Derivative, Higher-order derivatives
About this page
| Tag | 084NGSTWM7 |
|---|---|
| URI | m2://084NGSTWM7 |
| Kind | definition |
| Writing | W0 stub |
| MSC | 26A24 |
| Defines | Higher derivative |
| Uses | Derivative function |
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