vastfish.blogg.se - Product rule calculus tufts

Ĭlick HERE to see a detailed solution to problem 21.Ĭlick HERE to return to the original list of various types of calculus problems. With tangent lines parallel to the line y + x = 12. PROBLEM 21 : Find all points ( x, y) on the graph of.

PROBLEM 20 : Find an equation of the line perpendicular to the graph ofĬlick HERE to see a detailed solution to problem 20.

PROBLEM 19 : Find an equation of the line tangent to the graph ofĬlick HERE to see a detailed solution to problem 19.

For what values of x is f'( x) = 0 ?Ĭlick HERE to see a detailed solution to problem 18. Compare it with the ordinary product rule to see the similarities and differences.Ĭlick HERE to see a detailed solution to problem 16.Ĭlick HERE to see a detailed solution to problem 17. For what values of x is f'( x) = 0 ?Ĭlick HERE to see a detailed solution to problem 15. For what values of x is f'( x) = 0 ?Ĭlick HERE to see a detailed solution to problem 14. For what values of x is f'( x) = 0 ?Ĭlick HERE to see a detailed solution to problem 13. The following problems require use of the chain rule.Ĭlick HERE to see a detailed solution to problem 7.Ĭlick HERE to see a detailed solution to problem 8.Ĭlick HERE to see a detailed solution to problem 9.Ĭlick HERE to see a detailed solution to problem 10.Ĭlick HERE to see a detailed solution to problem 11.Ĭlick HERE to see a detailed solution to problem 12. In most cases, final answers to the following problems are given in the most simplified form.Ĭlick HERE to see a detailed solution to problem 1.Ĭlick HERE to see a detailed solution to problem 2.Ĭlick HERE to see a detailed solution to problem 3.Ĭlick HERE to see a detailed solution to problem 4.Ĭlick HERE to see a detailed solution to problem 5.Ĭlick HERE to see a detailed solution to problem 6. In the list of problems which follows, most problems are average and a few are somewhat challenging. Each time, differentiate a different function in the product and add the two terms together. The rule follows from the limit definition of derivative and is given by

The product rule is a formal rule for differentiating problems where one function is multiplied by another. In the following discussion and solutions the derivative of a function h( x) will be denoted by or h'( x). There is also an excellent Calc III review sheet made by a friend of mine from the University of Connecticut, which I have also included here.The following problems require the use of the product rule. The content is based on MATH 13 at Tufts University and follows closely the text of Calculus – Early Transcendentals by Briggs and Cochran.Ĭhapter 11 – Vectors and Vector-Valued Functionsġ1.1 – Vectors in the Plane, 11.2 – Vectors in Three Dimensions, 11.3 – Dot Products, 11.4 – Cross Products, 11.5 – Lines and Curves in Space, 11.6 – Calculus of Vector-Valued Functions, 11.7 – Motion in Space, and 11.8 – Length of CurvesĬhapter 12 – Functions of Several Variablesġ2.1 – Planes and Surfaces, 12.2 – Graphs and Level Curves, 12.4 – Partial Derivatives, 12.5 – The Chain Rule, 12.6 – Directional Derivatives and the Gradient, 12.7 – Tangent Planes and Linear Approximations, 12.8 – Maximum/Minimum Problems, 12.9 – Lagrange Multipliersġ3.1 – Double Integrals over Rectangular Regions, 13.2 – Double Integrals over General Regions, 13.3 – Double Integrals in Polar Coordinates, 13.4 – Triple Integrals, 13.5 – Triple Integrals in Cylindrical and Spherical Coordinatesġ4.1 – Vector Fields and Integrals, 14.2 – Line Integrals, 14.3 – Conservative FieldsĬhapter 14, Part II – Vector Calculus – Part IIġ4.4 – Green’s Theorem, 14.5 – Divergence and Curl, 14.6 – Surface Integrals, 14.7 – Stokes’ Theorem, 14.8 – Divergence Theorem The links below contain review material for an undergraduate-level course on multivariable calculus.