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Find $y^{\prime \prime}$ for the following functi…

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Maurizia D.

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Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48 Problem 49 Problem 50 Problem 51 Problem 52 Problem 53 Problem 54 Problem 55 Problem 56 Problem 57 Problem 58 Problem 59 Problem 60 Problem 61 Problem 62 Problem 63 Problem 64 Problem 65 Problem 66 Problem 67 Problem 68 Problem 69 Problem 70 Problem 71 Problem 72 Problem 73 Problem 74 Problem 75 Problem 76 Problem 77 Problem 78 Problem 79 Problem 80 Problem 81 Problem 82 Problem 83 Problem 84 Problem 85 Problem 86 Problem 87 Problem 88 Problem 88 Problem 90

Problem 57 Hard Difficulty

Find $y^{\prime \prime}$ for the following functions.
$$y=x \sin x$$

Answer

2 cos x - x sin x

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Calculus 1 / AB

Calculus Early Transcendentals

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Derivatives

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Video Transcript

this question asked us to find that the second derivative of X sign of X and because we have two different functions being multiplied together. We have to use the product rule so we can begin by defining our A and B terms. So for here we have a equaling X and a prime Equalling one and be equaling sign of X would be prime Equalling co sign of X. And now we can plug these values into our product will formula. So we'll have. Why Prime Equalling one times Sign it. X plus x Times Co Sign of X in this simplifies to sign of X plus x co Sign of X But notice here how this second term is also two different functions being multiplied together again. So you'd have to do the product rule another time so we can define our A term again to be X and a prime equaling one and Herbie Term equal and co sign of X would be prime equaling negative sign of X. And this time here, because it's just a sign function, we can automatically take its derivative. So the derivative of sign of X is co sign of X plus, and now we'll do the product rule. So one times co sign of X plus X times. Negative sign of X and let me simplify. We get co sign of X plus co Sign of X minus X sign of X, I notice. Here we have, like, terms so we can combine these two to get to co sign of X minus X sign of X.

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William Briggs, Lyle Cochran, Bernard Gillet

Calculus Early Transcendentals

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