Derivative of an Arctangent Function

Question

Find the derivative of $$y=\arctan\left(\frac{\sqrt{3*x+2}}{2*x-1}\right)$$. Express your answer in its unsimplified form.

Accepted Answer

$$y'=\frac{\frac{(2*x-1)*\left(\frac{3}{2*\sqrt{3*x+2}}\right)-2*\sqrt{3*x+2}}{(2*x-1)^2}}{1+\frac{3*x+2}{(2*x-1)^2}}$$

Answer

$$y'=\frac{\frac{(2*x-1)*\left(\frac{3}{2*\sqrt{3*x+2}}\right)+2*\sqrt{3*x+2}}{(2*x-1)^2}}{1+\frac{3*x+2}{(2*x-1)^2}}$$

Answer

$$y'=\frac{\frac{(2*x-1)*\left(\frac{3}{2*\sqrt{3*x+2}}\right)-2*\sqrt{3*x+2}}{(2*x-1)}}{1+\frac{3*x+2}{(2*x-1)^2}}$$

Answer

$$y'=\frac{\frac{3}{2*\sqrt{3*x+2}}-2}{(2*x-1)^2\left(1+\frac{3*x+2}{(2*x-1)^2}\right)}$$