Identify the function (f(x))
Apply the appropriate differentiation rule
Use the power rule: (frac{d}{dx}(x^n)=nx^{n-1})
Use the constant rule: (frac{d}{dx}(c)=0)
Use the constant multiple rule: (frac{d}{dx}[c f(x)] = c f'(x))
Use the sum rule: (frac{d}{dx}[f(x)+g(x)] = f'(x)+g'(x))
Use the difference rule: (frac{d}{dx}[f(x)-g(x)] = f'(x)-g'(x))
Use the product rule: (frac{d}{dx}[f(x)g(x)] = f'(x)g(x)+f(x)g'(x))
Use 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})
Use the chain rule: (frac{d}{dx}[f(g(x))] = f'(g(x))g'(x))
Differentiate term by term
Simplify the result
Substitute values if a specific point is needed
Check the derivative for correctness