Identify the function
Apply the power rule: d/dx(x^n) = n x^(n-1)
Apply the constant rule: d/dx(c) = 0
Apply the constant multiple rule: d/dx[c f(x)] = c f'(x)
Apply the sum and difference rules: d/dx[f(x) ± g(x)] = f'(x) ± g'(x)
Use the product rule: d/dx[f(x)g(x)] = f'(x)g(x) + f(x)g'(x)
Use the quotient rule: d/dx[f(x)/g(x)] = [g(x)f'(x) – f(x)g'(x)] / [g(x)]^2
Use the chain rule: d/dx[f(g(x))] = f'(g(x))g'(x)
Differentiate common functions using standard formulas
Simplify the result
Check for algebraic errors