KCET2022MathematicsDifferentiation
If y= (1+x^2 ) ⁻¹ x-x , then d y d x is
Options
- A2 x ⁻¹ x
- B⁻¹ x x
- Cx^2 ⁻¹ x
- Dx ⁻¹ x
Correct answer
A. 2 x ⁻¹ x
Step-by-step solution
Given, y= (1+x^2 ) ⁻¹ x-x Differentiating the given function w.r.t. x aligned d y d x & = (1+x^2 ) d d x ( ⁻¹ x )+ ⁻¹ x d d x (1+x^2 )- d d x (x) & = (1+x^2 ) 1 (1+x^2 ) + ⁻¹ x(2 x)-1 & =1+2 x ⁻¹ x-1=2 x ⁻¹ x aligned