Let f(x) = sin(x) + cos(x). What is the derivative of f(x) at x = π/4?

Core Concept

The derivative of sin(x) is cos(x), and the derivative of cos(x) is -sin(x). Therefore, f'(x) = cos(x) - sin(x). At x = π/4, f'(π/4) = cos(π/4) - sin(π/4) = √2/2 - √2/2 = 0. Option B is incorrect because it's the value of sin(π/4) or cos(π/4), not the derivative at that point. Option C is incorrect because it's the value of √2, which is 2 times the value of sin(π/4) or cos(π/4). Option D is incorrect because it's the negative of the value in option C.