I have a question regarding first order derivatives. If we consider the function $f : \mathbb{R}^2\rightarrow\mathbb{R}^3$ with $(x_1, x_2)\mapsto (x^2_1+ x_2, x^3_2, \cos{x_2})$. We have to calculate $f'(0)(a)$ and $f''(0)(a)(b)$ where $a = (a_1, a_2)$ and $b = (b_1, b_2).$
Can some one please tell me how one is supposed to tackle this problem. Thanks.