AP EAMCET2009MathematicsDifferentiation
x= 1- y 1+ y d y d x is equal to
Options
- A4 (x+1)^2
- B4(x-1) (1+x)^3
- Cx-1 (1+x)^3
- D4 (x+1)^3
Correct answer
B. 4(x-1) (1+x)^3
Step-by-step solution
Given, x 1 = 1- y 1+ y Applying componendo and dividendo, we get array rlrl & & 1+x 1-x = (1+ y )+(1- y ) (1+ y )-(1- y ) & 1+x 1-x = 2 2 y & & y= ( 1-x 1+x )^2 array On differentiating w.r.t. x , we get aligned d y d x & = -2(1+x)^2(1-x)-(1-x)^2 2(1+x) (1+x)^4 & = (1-x)(1+x)(-2-2 x-2+2 x) (1+x)^4 & = 4(x-1) (x+1)^3 aligned