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generallei
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The answer GENERALLEI has 1 possible clue(s) in existing crosswords.
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Possible Crossword Clues |
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Floral garland for whoever? |
Last Seen in these Crosswords & Puzzles |
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Aug 1 2010 New York Times |
Generallei might refer to |
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In calculus, the General Leibniz rule, named after Gottfried Wilhelm Leibniz, generalizes the product rule (which is also known as "Leibniz's rule"). It states that if * * * * f * * * {\displaystyle f} * and * * * * g * * * {\displaystyle g} * are * * * * n * * * {\displaystyle n} * -times differentiable functions, then the product * * * * f * g * * * {\displaystyle fg} * is also * * * * n * * * {\displaystyle n} * -times differentiable and its * * * * n * * * {\displaystyle n} * th derivative is given by* * * * ( * f * g * * ) * * ( * n * ) * * * ( * x * ) * = * * ∑ * * k * = * 0 * * * n * * * * * * ( * * * n * k * * * ) * * * * * f * * ( * n * − * k * ) * * * ( * x * ) * * g * * ( * k * ) * * * ( * x * ) * * * {\displaystyle (fg)^{(n)}(x)=\sum _{k=0}^{n}{n \choose k}f^{(n-k)}(x)g^{(k)}(x)} * where * * * * * * * ( * * * n * k * * * ) * * * * = * * * * n * ! * * * k * ! * ( * n * − * k * ) * ! * * * * * * {\displaystyle {n \choose k}={n! \over k!(n-k)!}} * is the binomial coefficient and * * * * * f * * ( * 0 * ) * * * ( * x * ) * = * f * ( * x * ) * * * {\displaystyle f^{(0)}(x)=f(x)} * . * This can be proved by using the product rule and mathematical induction (see proof below). |