If f (x) = 9x10 tan-1x, find f ' (x).

F (x) = 9x10tan-1 (x)

Use the product rule to derive.

Let g (x) = 9x10

Let h (x) = tan-1 (x)

Product rule:

f' (x) = g' (x) h (x) + g (x) h' (x)

f' (x) = 90x9tan-1 - [9x10 / (1 + x2) ]