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Example 31 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at June 2, 2023 by Teachoo
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Example 31 You are here
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Transcript
Example 31 Find 𝑑𝑦/𝑑𝑥 , if 𝑥 = 𝑎 cos𝜃, 𝑦 = 𝑎 sin θ.Here 𝑑𝑦/𝑑𝑥 = (𝑑𝑦/𝑑𝜃)/(𝑑𝑥/𝑑𝜃) Calculating 𝒅𝒚/𝒅𝜽 𝑦 = 𝑎 sin θ 𝑑𝑦/𝑑𝜃 = 𝑑(𝑎 sin 𝜃)/𝑑𝜃 𝑑𝑦/𝑑𝜃 = 𝒂 𝒄𝒐𝒔𝜽 Calculating 𝒅𝒙/𝒅𝜽 𝑦 = 𝑎 cos θ 𝑑𝑦/𝑑𝜃 = 𝑑(𝑎 cos 𝜃)/𝑑𝜃 𝑑𝑦/𝑑𝜃 = −𝒂 𝒔𝒊𝒏𝜽 Now, 𝑑𝑦/𝑑𝑥 = (𝑑𝑦/𝑑𝜃)/(𝑑𝑥/𝑑𝜃) 𝑑𝑦/𝑑𝑥 = (𝑎 cosθ)/(−𝑎 sinθ ) 𝒅𝒚/𝒅𝒙 = −𝐜𝐨𝐭𝛉
