Introduction to differentiation and basic derivative rules
Find derivative of f(x) = x⁴
Power rule: d/dx[xⁿ] = nxⁿ⁻¹
What is the derivative of a constant?
Derivative measures rate of change, and constants don't change
Find dy/dx for y = 3x² - 2x + 5
Apply power rule to each term and sum the derivatives
What does f'(x) represent geometrically?
Derivative at a point gives slope of tangent line to the curve at that point
Find derivative of f(x) = √x
√x = x^(1/2), so derivative = (1/2)x^(-1/2) = 1/(2√x)