What is the value of (x + y)^2y” if x = e^t sint and y = e^t cost?(a) x/2(y’ + y)(b) x/2(y’ – y)(c) 2(xy’ + y)(d) 2(xy’ – y)I got this question in examination.This key question is from Second Order Derivative in chapter Limits and Derivatives of Mathematics – Class 11

What is the value of (x + y)^2y” if x = e^t sint and y = e^t cost?(a

1.	What is the value of (x + y)^2y” if x = e^t sint and y = e^t cost?(a) x/2(y’ + y)(b) x/2(y’ – y)(c) 2(xy’ + y)(d) 2(xy’ – y)I got this question in examination.This key question is from Second Order Derivative in chapter Limits and Derivatives of Mathematics – Class 11
Answer» The CORRECT answer is (d) 2(xy’ – y) The best I can explain: Since, x = e^t sint and y = e^t COST Therefore, dx/dt = e^t sint + e^t cost = y + x And, dy/dt = e^t cost – e^t sint = y – x So, y’ = dy/dx = (dy/dt)/(dx/dt) = (y – x)/(y + x) Thus, y” = [(x + y)(y’ – 1) – (y – x)(y’ + 1)]/(x + y)^2 Or, (x + y)^2y” = (x + y – y + x)y’ – x – y + x = 2xy’ – 2y = 2(xy’ – y)

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