Question

Differantion of y=tan invers x/a solution

Answer 1

$y = tan^{-1}\frac{x}{a}$
We know,
if y = tan⁻¹f(x)
Then, dy/dx = 1/(1+f(x)²).df(x)/dx use this here,
$y = tan^{-1}\frac{x}{a}\\\\\frac{dy}{dx}=\frac{d(tan^{-1}\frac{x}{a})}{dx}\\=\frac{1}{1+(\frac{x}{a})^2}.\frac{d(\frac{x}{a})}{dx}\\=\frac{a}{a^2+x^2}$