You may quote without proof the chain rule, the product rule, and the quotient rule, but, if used, your working should include an explicit statement of each rule the first time it is used, and you should explicitly mention the rule (e.g., justify a step in your argument by saying “...using the chain rule”) each time it is used subsequently in your working. You may refer, without proof, to the linearity property of the derivative and to the fol-lowing standard results:d:(c) = 0,for constant cdxd(x") =п-1—D па" , for n 3D 1, 2, 3...dxd(sin x)COs x,dxd(cos x)sin x,= -dxd-(In x)1dxHowever you must state each time one of these results is used. You may not assumewithout proof any other derivatives. For example, you may not assume that (x – 1) = 1(this would have to be derived explicitly using the linearity property and the above results). III. If x = 2(1+ sin 0) and y = 3(0 – cos 0) find expressions forsin 0 and cos 0, simplifying your answers as appropriate.d²yanddx2in terms ofdx

In this question, concept of derivative is applied. Derivative The derivative expresses the rate of…

Answered: (I. If x = 2(1+ sin 0) and y = 3(0 –…

(I. If x = 2(1+ sin 0) and y = 3(0 – cos 0) find expressions for and in terms of sin 0 and cos 0, simplifying your answers as appropriate. dx²

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.5: Product-to-sum And Sum-to-product Formulas

Problem 34E

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Question

You may quote without proof the chain rule, the product rule, and the quotient rule, but, if used, your working should include an explicit statement of each rule the first time it is used, and you should explicitly mention the rule (e.g., justify a step in your argument by saying “...using the chain rule”) each time it is used subsequently in your working.