Elements of Trigonometry And Trigonometrical Analysis Preliminary to the Diffe

Cover Elements of Trigonometry And Trigonometrical Analysis Preliminary to the Diffe
Elements of Trigonometry And Trigonometrical Analysis Preliminary to the Diffe
De Morgan Augustus
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) We have hardly thought it necessary to state that if two functions be always the same in value, their derived functions must be the same in value. But (124. ) we must not take a limited form of one, and equate its derived function to that of a limited form of the other, without first ascertaining that our limited forms are really equals.
The derived function of a function of a function of x is thus found.
Let us suppose

fx^.. . F(x+h)—fx = limit of ^^-^ ~ ^^ X 1"^!^ of"— ^ — —r^ — ^

...

■^— li n Now h and H diminish without limit together, and the first limit would be D(j>x, but iha. Tfx is in the place of x. It is, therefore, what D(f)X becomes whenfx is written for x. The second limit is Dfx ; whence -r\ r- T\ /with . R afterwardsN ^ ^ Ji^fx = J)x^ = cosa;^ X bx'^: and so on.

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