Problem 1E: Use the Chain Rule to find dz/dt or dw/dt. 1. z=x2+y2+xy,x=sint,y=et Problem 2E: Use the Chain Rule to find dz/dt or dw/dt. 2. z=cos(x+4y),x=5t4,y=1/t Problem 3E: Use the Chain Rule to find dz/dt or dw/dt. 5. w = xey/z, x = t2, y = 1 t, z = 1 + 2t Problem 4E: Use the Chain Rule to find dz/dt or dw/dt. 6. w = ln x2+y2+z2, x = sin t, y = cos t, z = tan t Problem 5E: Use the Chain Rule to find z/s and z/t. 5. z=x2y3,x=scost,y=ssint Problem 6E: Use the Chain Rule to find z/s and z/t. 6. z=arcsin(xy),x=s2+t2,y=12st Problem 7E: Use the Chain Rule to find z/s and z/t. 11. z = er cos , r = st, = s2+t2 Problem 8E Problem 9E: If z = f(x, y), where f is differentiable, and... Problem 10E: Let W(s,t)=F(u(s,t),(s,t)), where F, u and are differentiable, and... Problem 11E: Suppose f is a differentiable function of x and y, and g(u, v) = f(eu + sin v, eu + cos v). Use the... Problem 12E: Suppose f is a differentiable function of x and y, and g(r,s)=f(2rs,s24r). Use the table of values... Problem 13E Problem 14E Problem 15E Problem 16E Problem 17E: Use the Chain Rule to find the indicated partial derivatives. 21. z = x4 + x2y, x = s + 2t u, y =... Problem 18E: Use the Chain Rule to find the indicated partial derivatives. 22. T=v2u+v, u = pqr, v = pqr;... Problem 19E: Use the Chain Rule to find the indicated partial derivatives. 23. w = xy + yz + zx, x = r cos, y = r... Problem 20E: Use the Chain Rule to find the indicated partial derivatives. 24. P=u2+v2+w2, u = xey, v = yex, w =... Problem 21E: Use the Chain Rule to find the indicated partial derivatives. 25. N=p+qp+r, p = u + vw, q = v + uw,... Problem 22E: Use Equation 6 to find dy/dx. 28. cos(xy) = 1 + sin y Problem 23E: Use Equation 6 to find dy/dx. 29. tan1(x2y) = x + xy2 Problem 24E: Use Equation 6 to find dy/dx. 30. ey sin x = x + xy Problem 25E: Use Equations 7 to find z/x and z/y. 31. x2 + 2y2 + 3z2 = 1 Problem 26E: Use Equations 7 to find z/y and z/y. 26. xyz=cos(x+y+z) Problem 27E: Use Equations 7 to find z/x and z/y. 33. ez = xyz Problem 28E: Use Equations 7 to find z/x and z/y. 34. yz + x ln y = z2 Problem 29E: The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its... Problem 30E Problem 31E: The speed of sound traveling through ocean water with salinity 35 purls per thousand has been... Problem 32E Problem 33E Problem 34E: The voltage V in a simple electrical circuit is slowly decreasing as the battery wears out. The... Problem 35E: The pressure of 1 mole of an ideal gas is increasing at a rate of 0.05 kPa/s and the temperature is... Problem 36E: A sound with frequency fs, is produced by a source traveling along a line with speed vs. If an... Problem 37E: Assume that all the given functions are differentiable. 45. If z = f (x, y), where x = r cos and y... Problem 38E: Assume that all the given functions are differentiable. 46. If u = f(x, y), where x = es cos t and y... Problem 39E: Assume that all the given functions are differentiable. 39. If z=f(xy), show that zx+zy=0. Problem 40E Problem 41E Problem 42E Problem 43E Problem 44E Problem 45E Problem 46E Problem 47E Problem 48E format_list_bulleted