It doesn't matter which way is chosen as long as the method is applied correctly. Some people find it easier to go one way or the other. Solution: f(x) sin2x 2sin(x) cos(x), by the sine double angle. You may select the number of problems, and the notation. The student will be given composite functions and will be asked to differentiate them using the chain rule. We get the same answer either way, so it doesn't matter which method we use. (a) Rewrite sin(2x) using the double-angle formula, then apply the product rule to find f/(x). These Calculus Worksheets will produce problems that involve using the chain rule to differentiate functions. Similarly, the chain rule makes it easy in the case that there are only $x$s in the denominator since this is "some function of $x$" raised to "some negative power".Ĭonsider $g(x) = \frac$$. Introduction In this unit we learn how to dierentiate a ‘function of a function’. Chain-Sine Rule y acos(u) dy dx asin(u)du dx Chain-Cosine Rule Ex2a. If there are $x$s only in the denominator, then the quotient rule will be very easy the lack of $x$s in the numerator makes the derivative of the numerator especially simple. The chain rule from single variable calculus has a direct analogue in multivariable calculus, where the derivative of each function is replaced by its. h z oMxabdJe g EwriZtah l vIJn qfei1nMi2tLe A TC 7a7l qc GuHlruPs 9. If there are $x$s only in the numerator, then there is no quotient and the result is straightforward. v G2r0Q1 H3O pK nu atEa 9 ZSVoGfutQw5a 5r Xe V RL xLpCW.8 Y hAnlQl0 vr liJgWh3t qsO drRe8s 5e Yrjv seTdr. Click HERE to return to the original list of various types of calculus problems. If there are $x$s in both places, then you (probably) will prefer to use the quotient rule. Click HERE to see a detailed solution to problem 21. A convenient feature of mathematics is that it works no matter which (valid) method you use.įor this kind of problem, it is easiest to ask yourself, "how many 'places' is there an $x$?" By "places", I mean "numerator and denominator". You select the formulation of the chain rule that you find easiest to use.
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