1. If $y=\tan ^{-1}\left(\frac{a+x}{1-a x}\right)$ find $\frac{d y}{d x}$
You asked:
Find the derivative of \(\operatorname{atan}{\left(\frac{a + x}{1 - a x} \right)}\) with respect to \(x\).
MathBot Answer:
\[\frac{d}{d x} y{\left(x \right)} = \frac{\frac{a \left(a + x\right)}{\left(1 - a x\right)^{2}} + \frac{1}{1 - a x}}{1 + \frac{\left(a + x\right)^{2}}{\left(1 - a x\right)^{2}}}\]