Please e-mail any correspondence to Duane Koubaīy clicking on the following address About this document. Your comments and suggestions are welcome. 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. (iv) the velocity with which the missile strikes the ground. For example, sin (x) is a composite function because it can be constructed as f (g (x)) for f (x)sin (x) and g (x)x. In other words, it helps us differentiate composite functions. (i) the initial velocity of the missile, (ii) the time when the height of the missile is a maximum. AP.CALC: FUN3 (EU), FUN3.C (LO), FUN3.C.1 (EK) Google Classroom About Transcript The chain rule states that the derivative of f (g (x)) is f' (g (x))g' (x). In the list of problems which follows, most problems are average and a few are somewhat challenging. Problem 1: A missile fired ground level rises x meters vertically upwards in t seconds and x 100t - (25/2)t 2. 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). The following problems require the use of the product rule.
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