5. DETAILS LARCALC11 2.5.019. Find dy/dx by implicit differentiation. y = sin xy dy/dx = 6. DETAILS LARCALC11 2.5.036. Find the slope of the tangent line to the graph at the given point. x3 + 13 - 6xy = 0, (4/3, 8/3) Folium of Descartes: 3(4/3, 8/3) -2 3 -1- -2 7. DETAILS LARCALC11 2.5.045. Use implicit differentiation to find an equation of the tangent line to the ellipse at the given point. * 2 yz 8 4 = 3, (4, 2)\f4 DETAILS LARCALC11 2.6.007. A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given values of x. y = 2x-+ 9; + 34 = 3 centimeters per second (a) x = -1 cm/sec (b) x=0 cm/sec ) x =1 cm/sec 5 DETAILS LARCALC11 2.6.011. The radius r of a circle is increasing at a rate of 7 centimeters per minute. Find the rate of change of the area when r = 29 centimeters. cm 6 DETAILS LARCALC11 2.6.013. The radius r of a sphere is increasing at a rate of 4 inches per minute. (a) Find the rate of change of the volume when r = 11 inches. in. /min (b) Find the rate of change of the volume when r = 34 inches. in. /minDETAILS LARCALC11 2.6.003. Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. y = Vx (a) Find dy/dt, given x = 4 and dx/dt = 6. dy/ dt = (b) Find dx/dt, given x = 49 and dy/dt = 3. dx/dt = 2 DETAILS LARCALC11 2.6.005. Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. xy = 8 (a) Find dy/dt, given x = 6 and dx/dt = 10. dy/dt = (b) Find dx/dt, given x = 1 and dy/dt = -7. dx/dt = 3 DETAILS LARCALC11 2.6.006. Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. x2 + y= = 169 (a) Find dy/dt, given x = 5, y = 12, and dx/dt = 5. dy/dt = (b) Find dx/dt, given x = 12, y = 5, and dy/dt = -5. dx/ dt =