What is the derivative of this function $y=sin^-1(sqrt(2t))$ ?

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Answer 1 · 2017-08-16T14:48:55

The derivative is $=1/(sqrt(2t(1-2t)))$

$y=arcsin(sqrt(2t))$

Therefore,

$siny=sqrt(2t)$

Differentiating with respect to $t$

$dy/dtcosy=1/(2sqrt(2t))*2 =1/sqrt(2t)$

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

$cos^2y=1-sin^2y=1-2t$

$cosy=sqrt(1-2t)$

$dy/dt=1/sqrt(2t)*1/sqrt(1-2t)$

What is the derivative of this function y=sin^-1(sqrt(2t))y=sin^-1(sqrt(2t))?