Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12

Last updated at March 10, 2021 by Teachoo
Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12
Transcript
Ex 5.3, 5 Find ๐๐ฆ/๐๐ฅ in, ๐ฅ2 + ๐ฅ๐ฆ + ๐ฆ2 = 100 ๐ฅ2 + ๐ฅ๐ฆ + ๐ฆ2 = 100 Differentiating both sides ๐ค.๐.๐ก.๐ฅ . ๐(๐ฅ2 + ๐ฅ๐ฆ + ๐ฆ2)/๐๐ฅ = (๐ (100))/๐๐ฅ ๐(๐ฅ2)/๐๐ฅ + ๐(๐ฅ๐ฆ)/๐๐ฅ + (๐(๐ฆ2))/๐๐ฅ = (๐ (100))/๐๐ฅ 2๐ฅ^(2โ1) + (๐(๐ฅ๐ฆ))/๐๐ฅ + (๐(๐ฆ2))/๐๐ฅ ร ๐๐ฆ/๐๐ฆ = 0 2๐ฅ + (๐(๐ฅ๐ฆ))/๐๐ฅ + (๐(๐ฆ2))/๐๐ฆ ร ๐๐ฆ/๐๐ฅ = 0 As (๐ฅ^๐ )^โฒ=๐๐ฅ^(๐โ1) & derivative of a constant is zero 2๐ฅ + (๐(๐ฅ๐ฆ))/๐๐ฅ + 2๐ฆ^(2โ1) . ๐๐ฆ/๐๐ฅ = 0 2๐ฅ + (๐(๐ฅ๐ฆ))/๐๐ฅ + 2๐ฆ . ๐๐ฆ/๐๐ฅ = 0 Using product rule in ๐ฅ๐ฆ = ๐ฅ^โฒ ๐ฆ+๐ฆ^โฒ ๐ฅ 2๐ฅ + ((๐(๐ฅ))/๐๐ฅ .๐ฆ+๐(๐ฆ)/๐๐ฅ.๐ฅ) + 2๐ฆ . ๐๐ฆ/๐๐ฅ = 0 2๐ฅ + (1 .๐ฆ+๐ฅ.๐(๐ฆ)/๐๐ฅ) + 2๐ฆ . ๐๐ฆ/๐๐ฅ = 0 2๐ฅ + ๐ฆ + ๐ฅ . ๐๐ฆ/๐๐ฅ + 2๐ฆ . ๐๐ฆ/๐๐ฅ = 0 (2๐ฅ + ๐ฆ) + ๐๐ฆ/๐๐ฅ . (๐ฅ + 2๐ฆ) = 0 ๐๐ฆ/๐๐ฅ . (๐ฅ + 2๐ฆ) = โ (2๐ฅ + ๐ฆ) ๐ ๐/๐ ๐ = (โ( ๐๐ + ๐ ))/( ( ๐ + ๐๐ ))
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