Derivatives

We are given the functions: $x%20%3D%20%5Csqrt%7B10%20%5Ccos%5E%7B-1%7D%20%5Ctheta%7D%2C%20%5Cquad%20y%20%3D%20%5Csqrt%7B10%20%5Csin%5E%7B-1%7D%20%5Ctheta%7D.$ To find $%5Cfrac%7Bdy%7D%7Bdx%7D$ , we will use the chain rule. First, differentiate $x$ and $y$ with respect to $%5Ctheta$ . For $x%20%3D%20%5Csqrt%7B10%20%5Ccos%5E%7B-1%7D%20%5Ctheta%7D$ , we differentiate with respect to $%5Ctheta$ : $%5Cfrac%7Bdx%7D%7Bd%5Ctheta%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ccdot%2010%5E%7B-1%2F2%7D%20%5Ccdot%20%5Cfrac%7Bd%7D%7Bd%5Ctheta%7D%20(%5Ccos%5E%7B-1%7D%20%5Ctheta)%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ccdot%20%5Cfrac%7B10%5E%7B1%2F2%7D%7D%7B1%20-%20%5Ctheta%5E2%7D.$ Similarly, for $y%20%3D%20%5Csqrt%7B10%20%5Csin%5E%7B-1%7D%20%5Ctheta%7D$ , we differentiate: $%5Cfrac%7Bdy%7D%7Bd%5Ctheta%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ccdot%2010%5E%7B-1%2F2%7D%20%5Ccdot%20%5Cfrac%7Bd%7D%7Bd%5Ctheta%7D%20(%5Csin%5E%7B-1%7D%20%5Ctheta)%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ccdot%20%5Cfrac%7B10%5E%7B1%2F2%7D%7D%7B%5Csqrt%7B1%20-%20%5Ctheta%5E2%7D%7D.$ Now, $%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7Bdy%7D%7Bd%5Ctheta%7D%20%5Cdiv%20%5Cfrac%7Bdx%7D%7Bd%5Ctheta%7D$ : $%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B%5Cfrac%7B1%7D%7B2%7D%20%5Ccdot%20%5Cfrac%7B10%5E%7B1%2F2%7D%7D%7B%5Csqrt%7B1%20-%20%5Ctheta%5E2%7D%7D%7D%7B%5Cfrac%7B1%7D%7B2%7D%20%5Ccdot%20%5Cfrac%7B10%5E%7B1%2F2%7D%7D%7B1%20-%20%5Ctheta%5E2%7D%7D%20%3D%20%5Cfrac%7B-y%7D%7Bx%7D.$

So, the correct option is (E) : $%5Cfrac%7B-y%7D%7Bx%7D$

High-Yield Trend

Chapter Questions
3 MCQs

Official Solution

Official Solution

Official Solution

Derivatives

High-Yield Trend

Chapter Questions 3 MCQs

Official Solution

Official Solution

Official Solution

Chapter Questions
3 MCQs