Question

Find the weak derivative of f(x)=∣sinx∣. 2)

Answer 1

The weak derivative of f(x) = |sin(x)| can be found by considering the left and right limits of the difference quotient. For x > 0, the derivative is sin(x), for x < 0, the derivative is -sin(x), and at x = 0, the derivative is undefined.

Step-by-step explanation:

The weak derivative of f(x) = |sin(x)| can be found by considering the left and right limits of the difference quotient. Using the definition of the absolute value function and the chain rule of differentiation, we can determine the weak derivative as follows:

1. For x > 0, f'(x) = sin(x).
2. For x < 0, f'(x) = -sin(x).
3. At x = 0, the left and right limits do not exist, so the weak derivative is undefined at x = 0.

Therefore, the weak derivative of f(x) = |sin(x)| is:

f'(x) = { sin(x), x > 0 }

f'(x) = { -sin(x), x < 0 }

f'(x) = undefined, x = 0