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Find the derivatives of the following: x = atacos3t ; y = atasin3t

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प्रश्न

Find the derivatives of the following:

x = `"a" cos^3"t"` ; y = `"a" sin^3"t"`

बेरीज
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उत्तर

x = a cost , y = a sin3t

`("d"x)/("d"t) = 3"a"cos^2"t" (- sin"t")`, `("d"y)/("dt") = 3 "a"sin^2"t"  (cos "t")`

`(("d"y)/("dt"))/(("d"x)/("dt")) = (3"a" sin^2"t" cos"t")/(- 3"a" cos^2"t" sin"t")`

`("d"y)/("d"x) = - (sin "t")/(cos "t")`

`("d"y)/("d"x)` = – tan t

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Differentiation Rules
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.4 [पृष्ठ १७६]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.4 | Q 13 | पृष्ठ १७६

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