(Solved): Chapter 6 Applications of the Derivative 29. ln(x+y)=x3y2+ln(x2+2)4;(1,2) 40. The graph of 2 dou ...

Chapter 6 Applications of the Derivative 29. $\ln (x+y)=x^3{y}^2+\ln \left(x^2+2\right)-4;(1,2)$ 40. The graph of 2 double folium. $(2,1)$. 30. $\ln \left(x^2+y^2\right)=\ln 5x+\frac{y}{x}-2$ In Exercises 31-36, find the equation of the tangent line at the given value of $x$ on each curve. 31. $y^3+xy-y=8x^4;x=1$ 32. $y^3+2x^{2}y-8y=x^3+19;x=2$ 33. $y^3+x{y}^2+1=x+2y^2;x=2$ 34. $y^4(1-x)+xy=2;x=1$ 35. $2y^3(x-3)+x\sqrt{y}=3;x=3$ 36. $\frac{y}{18}\left(x^2-64\right)+x^{2/3}{y}^{1/3}=12;x=8$ Information on curves in Exercises 37-40, as well as many other curves, is available on the Famous Curves section of the MacTutor History of Mathematics Archive website at www-history.mcs .st-and.ac.uk/ history. 37. The graph of $x^{2/3}+y^{2/3}=2$, shown in the figure, is an astroid. 41. The graph origin and Find the equation of the tangent line at the point $(1,1)$. (a) Write $x=$ (b) Grap 42. Much has $y\uparrow$ their role