- 期刊
Theorem on the Differentiation of a Composite Function with a Vector Argument
並列摘要
The paper provides a theorem on the differentiation of a composite function with a vector argument. The theorem shows how the partial derivative of the total derivative of the composite function can be expressed through the total derivative of the partial derivative of the composite function. The proof of the theorem is based on Mishkov's formula, which is the generalization of the well-known Faà di Bruno's formula for a composite function with a vector argument.
延伸閱讀
- Kivinukk, A., Saksa, A., & Zeltser, M. (2017). On approximation processes defined by a cosine operator function. Proceedings of the Estonian Academy of Sciences, 66(2), 214-224. https://doi.org/10.3176/proc.2017.2.11
- Merkes, E. P. (1980). A COVERING THEOREM FOR ODD TYPICALLY-REAL FUNCTIONS. International Journal of Mathematics and Mathematical Sciences, 1980(), 189-192. https://doi.org/10.1155/S0161171280000130
- Moak, D. S. (1984). AN APPLICATION OF HYPERGEOMETRIC FUNCTIONS TO A PROBLEM IN FUNCTION THEORY. International Journal of Mathematics and Mathematical Sciences, 1984(), 503-506. https://doi.org/10.1155/S0161171284000545
- Ng, S. M. (1979). Some theorems in approximation theory [master's thesis, The University of Hong Kong]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0029-1812201200005404
- GAUR, A. (1990). A THEOREM FOR FOURIER COEFFICIENTS OF A FUNCTION OF CLASS L^p. International Journal of Mathematics and Mathematical Sciences, 1990(), 721-725. https://doi.org/10.1155/S0161171290000977