Identify the function (f(x))
Choose the differentiation rule that applies
Apply the power rule: (frac{d}{dx}(x^n)=nx^{n-1})
Apply the constant rule: (frac{d}{dx}(c)=0)
Apply the constant multiple rule: (frac{d}{dx}[c,f(x)]=c,f'(x))
Apply the sum and difference rules: (frac{d}{dx}[f(x)pm g(x)]=f'(x)pm g'(x))
Apply the product rule: (frac{d}{dx}[f(x)g(x)]=f'(x)g(x)+f(x)g'(x))
Apply the quotient rule: (frac{d}{dx}left[frac{f(x)}{g(x)}right]=frac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^2})
Apply the chain rule: (frac{d}{dx}[f(g(x))]=f'(g(x))g'(x))
Differentiate special functions using their known derivatives
Simplify the result
Check for algebraic errors
Verify the derivative at any required point if needed