Differentiate. f( x) = 3 - xex xtex f ' ( x ) = X Enhanced Feedback Please try again using the Quotient Rule, which states d [f ( x ) ] - 9( x ) [f ( x ) ] - f ( x ) [g (x) ] d(x ) Lg(x ). Note that you may also need to use the Product Rule, [f(x)g(x)] = f(x)-[g(x)] + g(x)-d [f(x) ]. [g(x) 12A plane flying horizontally at an altitude of 2 mi and a speed of 580 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 4 mi away from the station. (Round your answer to the nearest whole number.) x "W lEnhanced Feedback lPlease \"Y again. Keep in mind that distance : '/ (altitude)2 + (horizontal distance)2 (or y2 : x2 + 172 ). Differentiate with respect to t on both sides of the equation, using the Chain Rule, to solve for $14. The lgiven speed of the plane is %. A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward rst base with a speed of 20 W5. /\\ 90ft / (a) At what rate is his distance from second base decreasing when he is halfway to first base? (Round your answer to one decimal place.) E rs (b) At what rate is his distance from third base increasing at the same moment? (Round your answer to one decimal place.) Ems Find dy/dx by implicit differentiation. tan-1(5x2y) = x + 4xyz =MICH MIMIENCMIVOF(MANME & FPFANSNMNEA ARCHX FOCAL My ( E + X C A Not secure | webassign.net/web/Student/Assignment-Responses/submit?dep=27466239&tags=autosave#question3804351_12 27. [-/1 Points] DETAILS SCALCET8 3.3.035.MI. MY NOTES PRACTICE ANOTHER A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is x(t) = 4 cos(t), where t is in seconds and x is in centimeters. equilibrium position min (a) Find the velocity and acceleration at time t. V(t) = a(t) = (b) Find the position, velocity, and acceleration of the mass at time t = 51/6. x(STI Select- left In what direction is it moving at that time? right Since v(Sit ) 2 v 0, the particle is moving to the ---Select--. V Need Help? Read It Watch It Master It Submit Ancwar Type here to search O O 7 w 5:34 PM 9/24/2021Find y' and y". y = e\" sin(,6'x) ' em(,8cos,6x+asinx) \"'4: II it y\" = em( 25i11 x + {1,6 cosx) EEnhanced Feedback Please try again using a combination of the Product Rule and the Chain Rule. Use implicit differentiation to find an equation of the tangent line to the curve at the given point. 3! sin(8x) = X cos(2y), (Hi2, HM) Use implicit differentiation to find an equation of the tangent line to the curve at the given point. X2 + 3/2 = (2x2 + 4y2 X)2 (0, 0.25) (cardioid) The gure shows a lamp located three units to the right of the y-axis and a shadow created by the elliptical region x2 + 4y2 S 5. If the point (5, 0) is on the edge of the shadow, how far above the xaxis is the lamp located?
