Derivative of Inverse Function/Also presented as

Derivative of Inverse Function: Also presented as

When Leibniz's notation for derivatives $\paren {\dfrac {\d y} {\d x} }$ is being used, Derivative of Inverse Function is usually seen presented as:

$\dfrac {\d x} {\d y} = \dfrac 1 {\frac {\d y} {\d x} }$

or:

$\dfrac {\d x} {\d y} = \dfrac 1 {\d y / \d x}$

where:

$\dfrac {\d x} {\d y}$ is the derivative of $x$ with respect to $y$
$\dfrac {\d y} {\d x}$ is the derivative of $y$ with respect to $x$.

This must not be interpreted to mean that derivative can be treated as fractions; it is simply a convenient notation.


Sources

  • 1964: Milton Abramowitz and Irene A. Stegun: Handbook of Mathematical Functions ... (previous) ... (next): $3$: Elementary Analytic Methods: $3.3$ Rules for Differentiation and Integration: Leibniz's Theorem for Differentiation of a Product: $3.3.9$
  • 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 13$: General Rules of Differentiation: $13.12$
  • 1976: K. Weltner and W.J. Weber: Mathematics for Engineers and Scientists ... (previous) ... (next): $5$. Differential Calculus: Appendix: Differentiation Rules: $6.$ Inverse functions
  • 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 12.10$
  • 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): inverse function
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.