If y= ⁻¹ ( a ^2 x^4+ a ^4 ) , then d y ~d x is

Step-by-step solution

y= ⁻¹ ( a ^2 x^4+ a ^4 ) Put x^2= a ^2 aligned & = ⁻¹ ( x^2 a ^2 ) & y= ⁻¹ ( a ^2 a ^4 ^2 + a ^4 ) & y= ⁻¹ ( a ^2 a ^4 (1+ ^2 ) ) & y= ⁻¹ ( 1 ) & y= ⁻¹( ) & y= & y= ⁻¹ ( x^2 a ^2 ) aligned Differentiating w.r.t. x , we get aligned d y ~d x & = 1 1+ ( x^2 a ^2 )^2 d d x ( x^2 a ^2 ) & = a ^4 a ^4+x^4 2 x a ^2 & = 2 a ^2 x x^4+ a ^4 aligned