An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 112
... derivative of the derivative of a function is called the second derivative of the function ; the de- rivative of the second derivative is called the third derivative ; and so on . 166. Corollary . The derivative of a constant is zero ...
... derivative of the derivative of a function is called the second derivative of the function ; the de- rivative of the second derivative is called the third derivative ; and so on . 166. Corollary . The derivative of a constant is zero ...
Page 113
... derivative of the sum is u ' -U v + 2 which is obviously the sum of their derivatives . 169. Corollary . By reversing the sign of v , it may be shown , in the same way , that the derivative of the difference of two functions is the ...
... derivative of the sum is u ' -U v + 2 which is obviously the sum of their derivatives . 169. Corollary . By reversing the sign of v , it may be shown , in the same way , that the derivative of the difference of two functions is the ...
Page 114
... Derivative of a Power . power of a variable . To find the derivative of any Solution . Let the variable be a and the power a " , and let 6 differ infinitely little from a ; the derivative of an is then bn b - an • - a Now when bis equal ...
... Derivative of a Power . power of a variable . To find the derivative of any Solution . Let the variable be a and the power a " , and let 6 differ infinitely little from a ; the derivative of an is then bn b - an • - a Now when bis equal ...
Page 115
... derivative of the pro- duct of two functions . Solution . Let u and v be the functions , and U and V their derivatives ; then , since the derivative is the rate of change of the function to that of the variable , it is evident The ...
... derivative of the pro- duct of two functions . Solution . Let u and v be the functions , and U and V their derivatives ; then , since the derivative is the rate of change of the function to that of the variable , it is evident The ...
Page 116
... derivative of a product of two functions is equal to the sum of the two products obtained by multiplying each function by the derivative of the other function . 177. Corollary . The derivative of is , then , ( x — a ) n v n ( x − a ) n ...
... derivative of a product of two functions is equal to the sum of the two products obtained by multiplying each function by the derivative of the other function . 177. Corollary . The derivative of is , then , ( x — a ) n v n ( x − a ) n ...
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126 become zero 3d root arithmetical progression coefficient commensurable roots common difference contained continued fraction continued product Corollary deficient terms denote derivative Divide dividend division equal roots equal to zero equation x² factor Find the 3d Find the 4th Find the continued Find the greatest Find the number Find the square Find the sum Free the equation Geometrical Progression given equation given number gives greatest common divisor Hence imaginary roots last term least common multiple letter logarithm monomials multiplied number of real number of terms polynomial positive roots preceding article Problem quantities in example quotient radical quantities ratio real roots reduced remainder required equation required number row of signs Scholium Second Degree Solution Solve the equation square root Sturm's Theorem subtracted Theorem unity unknown quan unknown quantity variable whence