What is the derivative of $y = arctan (\sqrt{3} x^{2} - 1)$ $y= arctan (sqrt 3x^2 -1)$ ?

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Answer 1 · 2018-06-27T02:17:00

$y'=(2sqrt3x)/(1+(sqrt3x^2+1)^2)$

$color(blue)(d/dx)tan^-1u=((du)/dx)/(1+u^2)$

Let $u=sqrt3x^2-1$ , $(du)/dx=2sqrt3x$

$y'=(2sqrt3x)/(1+(sqrt3x^2+1)^2)$

What is the derivative of y= arctan (sqrt 3x^2 -1)y=arctan(√3x2−1)y= arctan (sqrt 3x^2 -1)?