Consider the following. x2 Z=X' + 1 -X - 7x2 Let u(x) = x2 and v(x) = 1 - x - 7x2. Find each indicated derivative. u'(x ) = V' ( X ) = Find each indicated product. v ( x ) . u' ( x ) = u ( x ) . v' ( x ) = Find az dx dz dx7 7v? 1 q We are asked to find dp , the first derivative, for p = d . Notice that the given function is the quotient of two differentiable functions of q. q v(x) - u'(x) u(x) - v'(x) Recall the Quotient Rule: If f(x) = \"EX; where u and v are differentiable functions of x, with v(x) at 0, then f'(x) = [v(x)]z v x If we let u(q) = 77V? and v(q) = 1 q, we can apply the Quotient Rule to find %. q Begin by finding the derivative of v(q). If v(q) = 1 q, then v'(q) = |:| . Before finding the derivative of u(q), it must be written in exponential form to use the Power Rule. Rewrite u(q) in exponential form. _ ' 1/7