Answer is: option2

\( -g'(a) \)

Solution:

We are given that \( g(x) \) is an even function, meaning:

\[ g(-x) = g(x) \quad \text{for all } x. \]

Since \( g(x) \) is even, we differentiate both sides with respect to \( x \):

\[ \frac{d}{dx} g(-x) = \frac{d}{dx} g(x). \]

Using the chain rule on the left-hand side:

\[ g'(-x) \cdot (-1) = g'(x). \]

Thus,

\[ g'(-x) = -g'(x). \]

Setting \( x = a \), we get:

\[ g'(-a) = -g'(a). \] Final Answer: \[ \boxed{-g'(a)} \]