Mathematics, 03.11.2020 16:30 wxvvyyyy
Prove that d dx (sinh−1(x)) = 1 1 + x2 . Solution 1 Let y = sinh−1(x). Then sinh(y) = x. If we differentiate this equation implicitly with respect to x, we get dy dx = 1. Since cosh2(y) − sinh2(y) = 1 and cosh(y) ≥ 0, we have cosh(y) = 1 + sinh2(y) , so dy dx = 1 cosh(y) = 1 1 + sinh2(y) = . Solution 2 From the equation sinh−1(x) = ln x + x2 + 1 , we have d dx (sinh−1(x)) = d dx ln x + x2 + 1 = 1 x + x2 + 1 d dx x + x2 + 1 = 1 x + x2+ 1 1 + x x2 + 1 = x2 + 1 + x x + x2 + 1 x2 + 1 = 1 x2 + 1 g
Answers: 2
Mathematics, 21.06.2019 15:10, sbelgirl2000
Figure abcde is a regular pentagon. segment ae is located at a (2, 1) and e (4, 1). what is the perimeter of abcde? 4 units 6 units 8 units 10 units
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Mathematics, 21.06.2019 23:30, hntnhtthnyt
Kerion has a beaded necklace business. she can make 12 necklaces is 2 hours. how long will it take her to make 9 necklaces?
Answers: 1
Prove that d dx (sinh−1(x)) = 1 1 + x2 . Solution 1 Let y = sinh−1(x). Then sinh(y) = x. If we diffe...
English, 05.12.2019 06:31