Recognizing opportunities to apply derivative rules can simplify differentiation. Calculate derivatives of familiar functions. Direct application of the definition of the derivative and specific rules can be used to calculate the derivative for functions of the form f(x) = x′. Sums, differences, and constant multiples of functions can be differentiated using derivative rules. The power rule combined with sum, difference, and constant multiple properties can be used to find the derivatives for polynomial functions. Calculate derivatives of products and quotients of differentiable functions. Derivatives of products of differentiable functions can be found using the product rule. Derivatives of quotients of differentiable functions can be found using the quotient rule. The chain rule provides a way to differentiate composite functions.