The conversation between human and AI assistant.
What is the derivative of y = x^1/2?
Can you explain how to derive it?
Sure! We use the power rule of differentiation, which states that if y = x^n, then dy/dx = nx^(n-1). For y = x^1/2, n = 1/2. Therefore, dy/dx = (1/2)x^(-1/2) which simplifies to 1/(2x^(1/2)).