Second Order Derivative

Step 1: Differentiate both sides Given: $y%20%3D%20(%5Ctan%5E%7B-1%7D%202x)%5E2%20%2B%20(%5Ccot%5E%7B-1%7D%202x)%5E2.$ Differentiate with respect to $x$ , $%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%202%20(%5Ctan%5E%7B-1%7D%202x)%20%5Ccdot%20%5Cfrac%7B1%7D%7B1%20%2B%20(2x)%5E2%7D%20%5Ccdot%202%20%2B%202%20(%5Ccot%5E%7B-1%7D%202x)%20%5Ccdot%20%5Cfrac%7B-1%7D%7B1%20%2B%20(2x)%5E2%7D%20%5Ccdot%202.$ Since, $%5Ctan%5E%7B-1%7D%20a%20%2B%20%5Ccot%5E%7B-1%7D%20a%20%3D%20%5Cfrac%7B%5Cpi%7D%7B2%7D%2C$ $%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%200.$ Step 2: Differentiate again $%5Cfrac%7Bd%5E2y%7D%7Bdx%5E2%7D%20%3D%20-%5Cfrac%7B8x%7D%7B(1%20%2B%204x%5E2)%5E2%7D.$ Multiplying by $(1%2B4x%5E2)%5E2$ and subtracting 16, $(1%2B4x%5E2)%5E2%20y''%20-%2016%20%3D%20-8x(1%20%2B%204x%5E2)%20y'.$

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Second Order Derivative

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs