50 DIFFERENTIAL CALCULUS ILLUSTRATIVE EXAMPLE 3. Differentiate y = a Sx *. . d , Solution. dx ax = Gxloga a? 3 ?. Ans. ILLUSTRATIVE EXAMPLE 4. Differentiate y = Solution. = b (e? + *) dx dx ~ * dx by IX by IV by IX a byX
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ILLUSTRATIVE EXAMPLE 5. Differentiate y = x e *. Solution. = e x x e " 1 (x) = e*x eX -* + x^ logx e x = e x x e *l- + logxj. Ans. . Logarithmic differentiation. Instead of applying VIII and at once in differentiating logarithmic functions, we may sometimes simplify the work by first making use of one of the formulas 7-10 on p. 1. Thus above Illustrative Example 2 may be solved as follows : ILLUSTRATIVE EXAMPLE 1. Differentiate y = log Vl x 2 . Solution. By using 10, p. 1, we may write this in a form free from radicals as follows : Then ay iS (1 -* 2) by Villa
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Ans. ILLUSTRATIVE EXAMPLE 2. Differentiate y = log- Solution. Simplifying by means of 10 and 8, p. 1, dx -X 2 x by VIII a, etc.
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