How do you take the derivative of $y=tan^-1 sqrt(3x)$ ?

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Answer 1 · 2018-07-14T04:30:11

$(dy)/(dx)=sqrt(3x)/(2x(1+3x))$

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

Recall if $y=tan^(-1)x$ , then $(dy)/(dx)=1/(1+x^2)$

$(dy)/(dx)=1/(1+(sqrt(3x))^2)times (sqrt3/(2sqrtx))$

$(dy)/(dx)=1/(1+3x)timessqrt(3x)/(2x)$

$(dy)/(dx)=sqrt(3x)/(2x(1+3x))$

How do you take the derivative of y=tan^-1 sqrt(3x)y=tan^-1 sqrt(3x)?