A Vest Pocket Handbook of Mathematics for Engineers

Cover A Vest Pocket Handbook of Mathematics for Engineers
A Vest Pocket Handbook of Mathematics for Engineers
L a Leslie Abram Waterbury
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d (cos x)= -sinx . Dx. d (tan x)=sec 2 x . Dx. d (cot x) = cosec 2 x . Dx. d (sec x) =sec x . Tan x . Dx. D (cosec x) = cosec x . Cot x . Dx. d (vers x) = d (1 - cos x) = +sin x . Dx. D (covers x)=d (l-sinx)= -cosx. Dx. J dtsin-x^dx/vT^ II d(cos- 1 x)=-dx/Vl-x 2 . Z < d (tan- 1 x)=dx/(l+x 2 ). d(cot~ 1 x)=-dx/(l+x 2 ). J eo d(sec- 1 x) = dx/(xV / x 2 -l). ; g ^ ^ d (vers- 1 x) = dx/v / 2 x-x 2 . 2 O d (covers - 1 x) = - dx/v^x-x 2 . _ H s ^ "*i To differentiate a junction : M 1. Find the value of the increment of the function in terms of the increments of its variables ; 2. Consider the increments to be infinitesi- mals, and in all sums drop the infinitesimals of higher order than the first, and in the 22 DIFFERENTIAL CALCULUS remaining terms substitute differentials for increments. For the maximum value of a function the first derivative is zero, and the second deriv- ative is negative. For the minimum value of a function the first derivative is zero, and the second deriva- tive is positive.

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