How do you find the derivative of the function: $arcsin(sqrt(2x-1))$ ?

Question

1954 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-25T14:29:12

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

Let $y=arcsin(sqrt(2x-1))$

Therefore,

$siny=sqrt(2x-1)$

Derivation with respect to $x$

$dy/dxcosy=2/(2sqrt(2x-1))=1/sqrt(2x-1)$

$dy/dx=1/sqrt(2x-1)*1/cosy$

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

$cos^2y=1-sin^2y=1-(2x-1)=2-2x$

$cosy=sqrt(2-2x)$

So,

$dy/dx=1/sqrt(2x-1)*1/sqrt(2-2x)$

How do you find the derivative of the function: arcsin(sqrt(2x-1))arcsin(sqrt(2x-1))?