What is Differentiable: Definition and 284 Discussions

In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non-vertical tangent line at each interior point in its domain. A differentiable function is smooth (the function is locally well approximated as a linear function at each interior point) and does not contain any break, angle, or cusp.
More generally, for x0 as an interior point in the domain of a function f, then f is said to be differentiable at x0 if and only if the derivative f ′(x0) exists. In other words, the graph of f has a non-vertical tangent line at the point (x0, f(x0)). The function f is also called locally linear at x0 as it is well approximated by a linear function near this point.

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  1. B

    Geometry William Boothby Introduction to Differentiable Manifolds

    I've been searching high and low through the Google for a solutions manual to William Boothby's "An Introduction to Differentiable Manifolds and Riemannian Geometry" to no avail. Does anyone know if ∃ such a thing? Thanks.
  2. B

    MHB Advanced Calculus - Differentiable and Converging Polynomials

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  3. V

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  4. V

    Find Null Paths in Differentiable Manifolds Using One-Forms

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  5. adoion

    Scalar field 2 dimensional discontinuous but differentiable

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  6. B

    Verifying Whether A Complex Function Is Differentiable

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  7. SixBooks

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  8. N

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  9. U

    Differentiable homework

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  10. U

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  11. binbagsss

    Differentiability and continously differentiable definition/concepts.

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  12. B

    Function over matrices, continuous and differentiable?

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  13. K

    Proving C is a Differentiable Function: Inverse Function Theorem & Chain Rule

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  14. L

    Continuously differentiable function

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  15. Demon117

    Show that differentiable curves have measure zero in R^2

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  16. V

    Showing a twice differentiable function is a vector space

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  17. L

    Where is the function differentiable

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  18. J

    MHB Show that f(x,y) is differentiable

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  19. V

    Inverse of a function is not differentiable

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  20. evinda

    MHB Is f(x) differentiable at x=0?

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  21. H

    How to prove whether a function is differentiable

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  22. F

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  23. F

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  24. F

    How does one show that the function is differentiable?

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  25. M

    MHB Show that the function is not differentiable at the point z

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  26. S

    What is the derivative equation for a continuously differentiable function?

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  27. C

    Differentiable function of 2 variables

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  28. F

    Differentiable functions in complex analysis

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  29. mnb96

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  30. mnb96

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  31. F

    Exercise: is f(x,y) continuous and differentiable?

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  32. PsychonautQQ

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  33. B

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  34. C

    Why are functions not differentiable at holes?

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  35. P

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  36. D

    2-dimensional differentiable surfaces

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  37. N

    Differentiable Linear Transformation

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  38. stripes

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  39. B

    Find where a complex function is differentiable

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  40. Z

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  41. J

    Chain rule question: if f is a differentiable function

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  42. S

    What happens with a differentiable function in the neighborhood of x?

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  43. I

    MHB Solve twice differentiable function

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  44. I

    MHB Proving Function Polynomial in Coordinates is Differentiable Everywhere

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  45. Y

    MHB For which parameter values the function is continuous and differentiable

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  46. J

    Proving that a solution to an IVP is unique and infinitely differentiable

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  47. micromass

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  48. C

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  49. K

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  50. C

    How to Determine Complex Differentiability and Holomorphicity of a Function?

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