
Last updated at May 29, 2018 by Teachoo
Transcript
Ex 5.7, 1 Find the second order derivatives of the function ๐ฅ^2 + 3๐ฅ + 2 Let ๐ฆ = ๐ฅ^2 + 3๐ฅ + 2 Differentiating ๐ค.๐.๐ก.๐ฅ ๐๐ฆ/๐๐ฅ = (๐(๐ฅ^2 + 3๐ฅ + 2))/(๐๐ฅ ) ๐๐ฆ/๐๐ฅ = (๐(๐ฅ^2))/๐๐ฅ + (๐(3๐ฅ) )/๐๐ฅ + (๐(2) )/๐๐ฅ ๐๐ฆ/๐๐ฅ = 2๐ฅ+3+0 ๐๐ฆ/๐๐ฅ = 2๐ฅ + 3 Again Differentiating ๐ค.๐.๐ก.๐ฅ ๐/๐๐ฅ (๐๐ฆ/๐๐ฅ) = (๐ (2๐ฅ + 3))/๐๐ฅ (๐^2 ๐ฆ)/ใ๐๐ฅใ^2 = ๐(2๐ฅ)/๐๐ฅ + ๐(3)/๐๐ฅ = 2 + 0 = 2 Thus, (๐ ^๐ ๐)/(๐ ๐^๐ ) = 2
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