Derivatives of Trig Functions

Question

If f(x) = 9x¹⁰ tan^-1x, find f '(x).

Options:

1. 90x⁹tan^-1x + 9x¹⁰ 
2. 90x⁹tan^-1x + 9x¹⁰tan^-2x
3. 90x⁹tan^-1x - 9x¹⁰ 
4. 90x⁹tan^-1x + 9x¹⁰ 

Answer 1

Use the product rule:

If you have f(x) = u(x) * v(x), then

f'(x) = v*u' + u*v'