Inverse functions and their derivatives:

Theorem: If inverse functions f and g can be defined by y = f(x) and x = g(y) and if f'(x) exists and f'(x) ≠ 0 then g'(y) = 1/f'(x). This result is written as, if dy/dx exists and dy/dx ≠ 0, then dy/dx = 1/(dy/dx) or dy/dx.dx/dy 1 or 

Result:          

Example: Find out dy/dx of

                (a). y = sin 2x                                       (b). y = cos 2x

                (c). y = x sin^-1 x                                    (d). y = a tan^-1 x

                (e). y = sec² x                                        (f). y = (log₂ x)²

Solution:       

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