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Contents
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Reciprocal Trigonometric Functions 
Derivatives
of the Reciprocal Functions
The
derivatives of the reciprocal trigonometric functions can be derived from the
derivatives of the sine and cosine functions.
The
quotient rule is used in all the above derivatives.
In
general,
Examples
 Differentiate
with respect to x:
(i)
cosec (2x + 3)
(ii) cot (x2 + 5x + 2)
(iii) exsecx
(iv) sec (sin 2x)
Solutions:
(i)
d/dx [cosec (2x + 3)] = -2 cosec (2x + 3). cot (2x + 3)
(ii)
d/dx [cot (x2 + 5x + 2)] = - (2x + 5) cosec2 (x2
+ 5x + 2)
(iii)
d/dx (exsecx) = exsecx (sec x + x. sec x. tan x)
= sec x.exsecx (1 + x .tan x)
(iv)
d/dx [sec (sin 2x)] = 2 cos 2x. sec (sin 2x). tan (sin 2x)
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