Question

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

Answer 1

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)]