A Qo M 6:28 PM a) Use the Product Rule to find the derivative of the given function. b) Find the derivative by multiplying the expressions first. y=x'. x3 ) Use the Product Rule to find the derivative of the function. Select the correct answer below and fill in the answer box(es) to complete your choice. O A. The derivative is ( D ( x 3 ) O B. The derivative is (x ) ( +x 3( O C. The derivative is ( ) (x3) + (5x4) D. The derivative is ( x3 + 5x4. O E. The derivative is ( b) Multiply the expressions. x.x3= (Simplify your answer.) Now take the derivative of the answer from the previous step and simplify the answer from part a. Check to make sure that the two results are the same. That is, dy using either approach, -all 48% 6:33 PM a) Use the Quotient Rule to find the derivative of the given function. b) Find the derivative by dividing the expressions first = for x = 0 a) Use the Quotient Rule to find the derivative of the given function. Select the correct answer below and fill in the answer box(es) to complete your choice. O A. The derivative is O B. The derivative is O C. The derivative is * # . ( x0 D- x B( O D. The derivative is b) Divide the expressions. (Simplify your answer.) Now take the derivative of the answer from the previous step and simplify the answer from part a. Check to make sure that the two results are the same. That is, using either approach, - dyall 47% 6:35 PM - 4x Find an equation of the tangent line to the graph of y =- at the origin and at the point (1, - 2). x2+ 1 The tangent to the curve at the origin is y = The tangent to the curve at the point (1. - 2) is y = (Simplify your answer.)Be alll 47% 6:38 PM An accessories company finds that the cost, in dollars, of producing x belts is given by C(x) =770 + 35x - 0.065x2. Find the rate at which average cost is changing when 175 belts have been produced. First, find the rate at which the average cost is changing when x belts have been produced. C'(x) = When 175 belts have been produced, the average cost is changing at - for each additional belt. (Round to four decimal places as needed.) (1) O dollars per belt O belts per dollar O dollars O belts: allll 41% 7:02 PM An accessories company finds that the cost and revenue, in dollars, of producing x belts is given by C(x) =710+ 38x - 0.063x" and R(x) = 35x 10 . respectively. Determine the rate at which the accessories company's average profit per belt is changing when 179 belts have been produced and sold. First, find the rate at which the average profit is changing when x belts have been produced. P'(x) = When 179 belts have been produced and sold, the average profit is changing at (1) for each additional belt (Round to four decimal places as needed.) (1) O belts per dollar O belts O dollars per belt dollarsX alll 41% 7:03 PM The population P, in thousands, of a small city is given by the following function, a) Find the growth rate where t is time in years. Answer parts a) through c) The growth rate is 500t P(t) = - 312 + 4 b) Find the population after 10 yr. The population is after 10 years. (Round to the nearest integer as needed.) 70- Q c) Find the growth rate at t = 10 yr. The growth rate at t = 10 yr is residents/yr. (Round to the nearest integer as needed.) 40- 30- 9 10 11 12
