“differentiation”的概念、定义、翻译、参考文献-科学参考

differentiation

Physics

The process of finding the derivative of a function in differential calculus. If y=f(x), the derivative of y, written dy/dx or f′(x), is equal to the limit as Δ‎x → 0 of [f(x+Δ‎x)−f(x)]/Δ‎x. In general, if y=xⁿ, then dy/dx=nxⁿ⁻¹. On a graph of y=f(x), the derivative dy/dx is the gradient of the tangent to the curve at the point x.

Mathematics

The process of obtaining the derived function f ′ from the function f, where f ′(x) is the derivative of f at x. (For the derivatives of certain common functions, see appendix 7.) From these many other functions can be differentiated using the following rules of differentiation:
1. (i) If h = kf, where k is a constant, then h′ = kf ′.
2. (ii) If h = f + g, then h = f ′ + g′.
3. (iii) The product rule: If h = fg, then h′ = fg′ + f ′g.
4. (iv) The quotient rule: If h = f/g and g(x) ≠ 0 for all x, then
  
  $h' = \frac{g f' - f g'}{g^{2}} .$
5. (v) The chain rule: If h(x) = (f ∘ g)(x) = f(g(x)) for all x, then h′(x) = f′(g(x))g′(x).

Astronomy

A geological process by which a magma separates into layers of igneous rock of differing density and composition within a body such as a planet or asteroid. On the planetary scale, differentiation typically produces a core, a mantle, and a crust.

Chemical Engineering

A mathematical process used to find the rate at which one variable changes with respect to another. The result of differentiation of a function of y = f(x) is dy/dx or f’(x) and called the derivative. On a graph of f(x), dy/dx is the slope of the tangent to the curve y = f(x) at that point. In general, the rule for differentiation is that where y = axⁿ than
$\frac{d y}{d x} = a n x^{n - 1}$

Tables of standard differentials are used for other forms of equation.

Biology

The changes by which more specialized cells arise from less specialized cells, so that tissues and organs with particular functions can form during embryonic development. Furthermore, certain cells, called stem cells, retain the ability to differentiate throughout the life of the organism so that tissues can be replaced or repaired (see regeneration). Plants also have undifferentiated tissues (see meristem) that give rise to the new tissues required for growth, a process that typically is lifelong. Whatever the type of organism, the specialization inherent in differentiation depends on sequential changes in the pattern of gene expression as cells undergo successive divisions. The mechanisms involved have been most intensively studied in experimental organisms, notably the fruit fly Drosophila. In this insect the general body plan is established in the early embryo by proteins called morphogens, which are encoded by maternal genes of follicle cells and diffuse into the developing embryo. The various morphogens set up a pattern of concentrations that activates genes in different zones of the embryo to different extents, creating the basic pattern of body segments. A class of genes within the embryo itself, the segment genes, further refine this pattern. Within each segment the differentiation of appendages, such as limbs, is controlled by homeotic genes.

Geology and Earth Sciences

See magmatic differentiation.

单词	differentiation
释义	differentiation Physics The process of finding the derivative of a function in differential calculus. If y=f(x), the derivative of y, written dy/dx or f′(x), is equal to the limit as Δ‎x → 0 of [f(x+Δ‎x)−f(x)]/Δ‎x. In general, if y=xⁿ, then dy/dx=nxⁿ⁻¹. On a graph of y=f(x), the derivative dy/dx is the gradient of the tangent to the curve at the point x. Mathematics The process of obtaining the derived function f ′ from the function f, where f ′(x) is the derivative of f at x. (For the derivatives of certain common functions, see appendix 7.) From these many other functions can be differentiated using the following rules of differentiation: (i) If h = kf, where k is a constant, then h′ = kf ′. (ii) If h = f + g, then h = f ′ + g′. (iii) The product rule: If h = fg, then h′ = fg′ + f ′g. (iv) The quotient rule: If h = f/g and g(x) ≠ 0 for all x, then $h' = \frac{g f' - f g'}{g^{2}} .$ (v) The chain rule: If h(x) = (f ∘ g)(x) = f(g(x)) for all x, then h′(x) = f′(g(x))g′(x). Astronomy A geological process by which a magma separates into layers of igneous rock of differing density and composition within a body such as a planet or asteroid. On the planetary scale, differentiation typically produces a core, a mantle, and a crust. Chemical Engineering A mathematical process used to find the rate at which one variable changes with respect to another. The result of differentiation of a function of y = f(x) is dy/dx or f’(x) and called the derivative. On a graph of f(x), dy/dx is the slope of the tangent to the curve y = f(x) at that point. In general, the rule for differentiation is that where y = axⁿ than $\frac{d y}{d x} = a n x^{n - 1}$ Tables of standard differentials are used for other forms of equation. Biology The changes by which more specialized cells arise from less specialized cells, so that tissues and organs with particular functions can form during embryonic development. Furthermore, certain cells, called stem cells, retain the ability to differentiate throughout the life of the organism so that tissues can be replaced or repaired (see regeneration). Plants also have undifferentiated tissues (see meristem) that give rise to the new tissues required for growth, a process that typically is lifelong. Whatever the type of organism, the specialization inherent in differentiation depends on sequential changes in the pattern of gene expression as cells undergo successive divisions. The mechanisms involved have been most intensively studied in experimental organisms, notably the fruit fly Drosophila. In this insect the general body plan is established in the early embryo by proteins called morphogens, which are encoded by maternal genes of follicle cells and diffuse into the developing embryo. The various morphogens set up a pattern of concentrations that activates genes in different zones of the embryo to different extents, creating the basic pattern of body segments. A class of genes within the embryo itself, the segment genes, further refine this pattern. Within each segment the differentiation of appendages, such as limbs, is controlled by homeotic genes. Geology and Earth Sciences See magmatic differentiation.
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