Differentiate inverse tangent functions, Mathematics

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Differentiate the following functions.

(a) f (t ) = 4 cos-1 (t ) -10 tan -1 (t )

(b)  y = √z sin -1 ( z )

Solution

(a) Not much to carry out with this one other than differentiates each term.

94_differentiates.png

 (b) Before using the product rule don't forget to convert the radical to fractional exponents

1071_differentiates1.png

Alternate Notation : There is some alternate notation i.e. used on occasion to denote the inverse trig functions. This notation is following,

sin -1 x = arcsin x                                        cos-1 x = arccos x                   

tan -1 x = arctan x                                       sec-1 x = arcsec x

cot -1 x =arccot x                                         csc-1 x = arccsc x


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