What is the derivative of this function $y=tan^-1(3x)$ ?

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Answer 1 · 2016-12-13T16:36:27

The answer is $=3/(1+9x^2)$

$y=tan^(-1)3x$

$:.tany=3x$

Differentiating

$sec^2y dy/dx=3$

$dy/dx=3/sec^2y=3cos^2y$

$sin^2y+cos^2y=1$

$tan^2y+1=sec^2y$

$sec^2y=1+9x^2$

$cos^2y=1/(1+9x^2)$

$:.dy/dx=3cos^2y=3/(1+9x^2)$

What is the derivative of this function y=tan^-1(3x)y=tan^-1(3x)?