MAC 2311C Lecture 2: 3.6 :Derivative of Log Functions

2. In xx + 1) 4xx -7 2) 5. 1n In Exercises 7 and 8, find dy/dx implicitly 8. In Exercises 9 and 10, find the second derivative of the funct 10. f 9,f(x) =z?(x + 1)-3x3 Exercises 4.5 See CalcChat.com tor tutor 回饉回Differentiating Logarithmic Functions In Exercises 1-22, find the derivative of the function. See Examples 1, 2, 3, and 4 回 3, y ln(x2 + 3) 7, y = (In x)4 9, f(x)-2x ln x 29. log 31. log 33. loga 6, y = In/1-2x 8, y = (In x2)2 In x 14, y=ln 13, y= In 37. 15. in 18 17

(1 point) Use Stokes' Theorem to evaluate curl F dS where F(x, y, z) 5ezy1-3ezij + 2x22k and S is the half of the ellipsoid 4x2 + y2 + 4z2-4 that lies to the right of the zz-plane, oriented in the direction of the positive y-axis Since the half ellipsoid is oriented in the direction of the positive y-axis the boundary curve must be transversed clockwise A parametriza r(t) = cos(t) i+ 0 when viewed from the left. tion for the boundary curve C can be given by: (use the most natural parametrization) curl F.dS dt curl F·dS If you don't get this in 3 tries, you can see a similar example (online). However, try to use this as a last resort or after you have already solved the problem. There are no See Similar Examples on the Exams!

4. +-7 points SCalcET8 10.1.AE.005 My Notes Ask Your Teacher EXAMPLE5 Sketch the curve with parametric equations x = 3 sin(t), y = 9 sin2(t). SOLUTION Observe that y = (3 sin(t))2-x2 and so the point (x, y) moves on the parabola y -x2. But note also that, since -1 s sin(t) s1 we have part of the parabola for whichSXS , so the parametric equations represent only the Since sin(t) is periodic, the point (x, y)-3 sin(t), moves back and forth )to(3, ) infinitely many times along the parabola from -3, -3 3 Video Example- Need Help?Read It Talk to a Tutor