What is the derivative of arcsin(x/3)?

1 Answer
Narad T.
Oct 18, 2016

dy/dx=1/sqrt(9-x^2)

Explanation:

If y=arcsin(x/3)
Then siny=x/3
Differentiating both sides
cosy dy/dx=1/3
To calculate cosy, use cos^2y+sin^2y=1
So cosy=sqrt(1-x^2/9)=sqrt(9-x^2)/3
And the answer is
dy/dx=1/(3cosy)=3/(3sqrt(9-x^2))=1/sqrt(9-x^2

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