Did I do this question right? If not can you show me where I made a mistake? Can you also explain how to do B in detail?

I am unable to open a file so please don't make the explanation a file.

Method 1: Use the relation between inverse functions and find the derivative with respect to x by implicit differentiation.

Derivative of Inverse Functions * 1) Use method #1 . Let f (x) = x -5x -8 and let g be the inverse function of f. Inverse ! (1 ,-12) ( 1-7 ) (a) Find f (1) and f' (1). Inverse: x = 43 - 542-8 -> (1, -1 (-12, 1) (-7, 1) (b) Find g (-12) and g'(-12). dy ( x = y 3 - 542 - 8) a) f ( 1 ) = 1 - 5 (1) - 8 fi ( * ) = 3 x 2 - lox = 1-5-8 f' ( 1 ) = 3(1) - 10 ( 1 ) 1 = 342 24 - ax - logdy = -12 f= -7 1 = dy dx By2 - loy b) d4 5-2 1 dy dx 3- 10 = dx - 342-10y