If y= ⁻¹ ( 3+2 x 2-3 x )+ ⁻¹ ( 3 x 1+4 x^2 ) , then d y ~d x is equal to

Step-by-step solution

aligned y & = ⁻¹ ( 3+2 x 2-3 x )+ ⁻¹ ( 3 x 1+4 x^2 ) & = ⁻¹ ( 3 2 +x 1- 3 2 x )+ ⁻¹ ( 4 x-x 1+(4 x)(x) ) aligned aligned & = ⁻¹ ( 3 2 )+ ⁻¹ x+ ⁻¹ 4 x- ⁻¹ x y & = ⁻¹ ( 3 2 )+ ⁻¹(4 x) aligned Differentiating w.r.t. x , we get aligned & d y ~d x =0+ 4 1+(4 x)^2 & ~d y ~d x = 4 1+16 x^2 aligned