Alright so from my understanding MacLaurin is a special case of Taylor Series but at f(0). However my question involves solving the third degree of MacLaurin for
$$f(x) = sin(a \times x)\times cos(b\times x) $$
at some given values
First I calculated the first derivative
$$f'(x)=[a\times cos(ax) \times cos(bx)] - [b\times sin(ax)\times sin(bx)]$$
$$f''(x) = [-(a^2+b^2) \times sin(ax)\times cos(bx)] - [2 a b \times cos(ax) \times sin(bx)]$$
$$f'''(x) = [b(3a^2+b^2)\times sin(ax) \times sin(bx)] - [a(a^2+3b^2)\times cos(ax)\times cos(bx)]$$
MacLaurin third degree
$$f(0) = f(0) + f'(0)*(x) + f''(0)*(x)^2/2! + f'''(0) * (x)^3 / 3!$$
Okay so now to the problem, this up here should be of MacLaurin third degree, but I still got a x to use from the assignment, so I'm not sure if I should use that x from the start since it's actually defined as $f(x)$, it feels like I've tried everything but it just wont calculate correctly.
Numbers have been switched from the ones used in the assignment, I don't want just an answer, I want to learn how to do this.