Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Сторінка ix
... Functions IL Successive Differentiation ........ III . Change of the Independent variable IV . Elimination of Constants and Functions PAGE 1 9 28 43 V. Application of the Differential Calculus to the Development of Functions 52 22 VI ...
... Functions IL Successive Differentiation ........ III . Change of the Independent variable IV . Elimination of Constants and Functions PAGE 1 9 28 43 V. Application of the Differential Calculus to the Development of Functions 52 22 VI ...
Сторінка 1
... function of x , which is of a com- plicated form , it may generally be reduced to the differen- tiation of simpler functions by means of the theorem du = du dy dx dy dx ' y being some function of x , and u some function of y . This ...
... function of x , which is of a com- plicated form , it may generally be reduced to the differen- tiation of simpler functions by means of the theorem du = du dy dx dy dx ' y being some function of x , and u some function of y . This ...
Сторінка 4
... function consists of products and quotients of roots and powers , it is generally most convenient to take the differential of the logarithm , or , as it is usually called , the logarithmic differential of the function . ( 31 ) Let u ...
... function consists of products and quotients of roots and powers , it is generally most convenient to take the differential of the logarithm , or , as it is usually called , the logarithmic differential of the function . ( 31 ) Let u ...
Сторінка 5
... Functions of Two Variables . If u = 0 be an implicit function of two variables and y , then du dy dx dx du dy ( 43 ) Let ( 44 ) ( 45 ) DIFFERENTIATION . 5.
... Functions of Two Variables . If u = 0 be an implicit function of two variables and y , then du dy dx dx du dy ( 43 ) Let ( 44 ) ( 45 ) DIFFERENTIATION . 5.
Сторінка 14
... function of æ . Then making u = X , v = € 12 , d ' ( uv ) dx " = 6 Jdr X 1 X r ( r − 1 ) 1.2 dr - 2X a + & c . dx- -2 = Ex { ( ~ 1 ) d d 1 r ( r− 1 ) d r -- 2 + r.a + + & c . X dx 1.2 da = d dx Whence it appears that + a X. d d + a X ...
... function of æ . Then making u = X , v = € 12 , d ' ( uv ) dx " = 6 Jdr X 1 X r ( r − 1 ) 1.2 dr - 2X a + & c . dx- -2 = Ex { ( ~ 1 ) d d 1 r ( r− 1 ) d r -- 2 + r.a + + & c . X dx 1.2 da = d dx Whence it appears that + a X. d d + a X ...
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a² b2 a²x² angle arbitrary constant assume asymptote becomes branches C₁ Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx dx dy dx dx² dy dx dy dy dy dy dz dz dz eliminate ellipse equal Euler factor formula fraction function Geometry gives Hence hypocycloid infinite intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral Multiply negative origin parabola perpendicular radius SECT singular points singular solution spiral Substituting subtangent surface tangent plane theorem triangle University of Cambridge vanish whence x²)³