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.

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

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