Question

Find `dy/dx` if `y = tan^(-1) ((5x+ 1)/(3-x-6x^2))`

Answer 1

Let `y = tan^(-1)  ((5x+ 1)/(3-x-6x^2))`

`= tan^(-1) ((5x+1)/(1+2-x-6x^2))`

`= tan^(-1) ((5x+ 1)/(1-(3x + 2)(2x-11)))`

`= tan^(-1) (((3x+2)+(2x-1))/((1-(3x+2))(2x-1)))`

`y = tan^(-1)(3x + 2) + tan^(-1) (2x - 1)`

Differentiate w.r.t. x

`:. dy/dx = 3/(1+(3x+2)^2) + 2/(1+(2x-1)^2)`

`= 3/(1+9x^2+12x+ 4)+ 2/(1+4x^2-4x +1)`

`= 3/(9x^2+12x+5) + 1/(2x^2-2x+1)`