 The derivative of the product of two functions is equal to the first function times the derivative of the second plus the second times the derivative of the first.  Elementary Analysis - Page 116by Percey Franklyn Smith, William Anthony Granville - 1910 - 223 pagesFull view - About this book
 | Horatio Scott Carslaw - Calculus - 1905 - 142 pages
...dx r dx w ax In the case of two functions it is easy to remember that the differential coefficient of the product of two functions is equal to the first function x the differential coefficient of the second + the second function x the differential coefflcient of... | |
 | William Anthony Granville - Calculus - 1911 - 492 pages
...when AJT *0, An *0, and (AU — \ , 0. 1 d dv du T .'. — (uv) = u — + v — • dx^ } dx dx The derivative of the product of two functions is equal...second function times the derivative of the first. 39. Differentiation of the product of any finite number of functions. Now in dividing both sides of... | |
 | Ellery Williams Davis, William Charles Brenke - Calculus - 1912 - 514 pages
...Derivative of a Product. — The following rule is often useful in simplifying differentiations : Tlie derivative of the product of two functions is equal to the first factor times the derivative of the second plus the second factor times the derivative of the first... | |
 | Clyde Elton Love - Calculus - 1916 - 390 pages
...: (2) The derivative of the sum of two functions is equal to the sum of their derivatives. (3) The derivative of the product of two functions is equal...times the derivative of the second plus the second times the derivative of the first. (4) The derivative of the quotient of two functions is equal to... | |
 | Clyde Elton Love - Calculus - 1916 - 380 pages
...: (2) The derivative of the sum of two functions is equal to the sum of their derivatives. (3) The derivative of the product of two functions is equal...times the derivative of the second plus the second times the derivative of the first. (4) The derivative of the quotient of two functions is equal to... | |
 | Herman William March, Henry Charles Wolff - Calculus - 1917 - 434 pages
...Ax Ax Ax Ax Since AM approaches zero as Ax approaches zero, dy_ — <to du dx ~ dx dx or d(uv) dv du derivative of the product of two functions is equal to the first times the derivative of the second plus the second times the derivative of the first. Illustrations.... | |
 | Raymond Benedict McClenon - Functions - 1918 - 264 pages
...the limit of the second factor is 0. lir_ •=0 Ax Therefore lim — = uDxv + vDxu. QED In words, The derivative of the product of two functions is equal to the first times the derivative of the second, plus the second times the derivative of the first. Evidently this... | |
 | Claude Irwin Palmer, William Charles Krathwohl - Geometry, Analytic - 1921 - 374 pages
...Ax, - = Wl - + Vl - + Аи -. Let Дх = 0 and notice that Дмт^ also approaches zero as Or, the derivative of the product of two functions is equal to the first times the derivative of the second plus the second times the derivative of the first. Example.— If... | |
 | Claude Irwin Palmer - Calculus - 1924 - 476 pages
...also approaches zero as ¿лХ a limit, then fin d(uv) dv . du [7] л ;. = ur + VT-- dz dx dz Or, the derivative of the product of two functions is equal to the first times the derivative o} the second plus the second times the derivative of the first. Example. If y... | |
 | K. F. Riley - Mathematics - 1974 - 556 pages
...assumptions about the specific forms/, g and h, other than/(x) = g(x)h(x). In words, the result reads, The derivative of the product of two functions is equal...second function times the derivative of the first). For the example /(x) = x3 sin x given earlier, (1.41) gives — (x3 sin x) = x3 ^- (sin x) + sin x... | |
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