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

Question

1772 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)#