How do you differentiate $g(x) = 2arcsin(e^(3x))$ ?

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Answer 1 · 2017-05-26T17:26:36

$g'(x) = (6e^(3x))/sqrt(1-e^(6x))$

Let $g(x) = y$

$y= 2arcsin(e^(3x))$

$1/2y= arcsin(e^(3x))$

$sin(1/2y) = e^(3x)$

$(1/2cos(1/2y))(dy/dx) = 3e^(3x)$

$dy/dx = (6e^(3x))/cos(1/2y)$

$cos(1/2y) = sqrt(1-sin^2(1/2y)) = sqrt (1-e^(6x))$

$dy/dx = (6e^(3x))/sqrt(1-e^(6x))$

How do you differentiate g(x) = 2arcsin(e^(3x)) g(x) = 2arcsin(e^(3x)) ?