This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise dx Calculate -. Simplify your answer. HINT [See Examples 1 and 2.] Step 1 In the given equation y X we have the quotient of two differentiable functions of x: |x| and x . Therefore, to differentiate we must first recall the Quotient Rule which states that if f and g are differentiable functions of x, then so is their quotient ., and the following formula applies, provided that g(x) # 0. d F(x) F'(x)g(x) - f(x)g'(x) dx 9 ( x ) [g(x) 12 Many like to remember that the derivative of a quotient is the derivative of the top function times the bottom function minus the top function times the derivative of the bottom function, all over the bottom function squared. derivative of derivative of top bottom top bottom d F ( x ) F' (x ) g (x) - F(x ) g'(x ) dx 9 (x ) [g(x) 12 bottom squared For the given equation y if we let f(x) = Ixl and g(x) = x , then y = In other words, we can define f(x) = Ixl as the top function and g(x) = x as the bottom function. X ? g(x ) Note that since y is the quotient of two differentiable functions, we can use the quotient rule to find the derivative of y with respect to x of - As a precursor to using the quotient rule, complete the following statements. If f(x) = Ixl, then f'(x) = If g(x) - x , then g'(x) = 7x