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
![1408_Inverse functions and their derivatives.png](https://www.expertsmind.com/../CMSImages/1408_Inverse functions and their derivatives.png)
Result:
![1889_Inverse functions and their derivatives1.png](https://www.expertsmind.com/../CMSImages/1889_Inverse functions and their derivatives1.png)
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:
![1849_Inverse functions and their derivatives2.png](https://www.expertsmind.com/CMSImages/1849_Inverse%20functions%20and%20their%20derivatives2.png)
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