found, that of the corresponding inverse function is easily deduced by means of the theorem of Art. 58. For let x=f(y), and therefore y=ƒ ̃1(x); then 6. y=ev", where u = log sin v, and v = (sin w)", and w = x2. The results of any preceding examples may be assumed. CHAPTER III. STANDARD FORMS. 63. It is the object of the present Chapter to investigate and tabulate the results of differentiating the several standard forms referred to in Art. 40. We shall always consider angles to be measured in circular measure, and all logarithms to be Napierian, unless the contrary is expressly stated. It will be remembered that if u = p(x), then, by the definition of a differential coefficient, Now, since h is to be ultimately zero, we may h consider to be less than unity, and we can therefore х D h\n apply the Binomial Theorem to expand (1+1)", what ever be the value of n; hence 65. If it be required to find the differential coefficient of " without the use of the Binomial Theorem we quote the result of Art. 23, |