How do I find the derivative of y = (arcsin(x))^-1?

1 Answer
Bill K.
Jun 26, 2015

dy/dx=-(arcsin(x))^(-2)* 1/sqrt{1-x^2}=-1/(arcsin^{2}(x)sqrt{1-x^2})

Explanation:

Use the Chain Rule: d/dx(f(g(x)))=f'(g(x))*g'(x) with f(x)=x^{-1} and g(x)=arcsin(x). Since f'(x)=-x^{-2}=-1/x^2 and g'(x)=1/sqrt{1-x^2}, it follows that

d/dx((arcsin(x))^{-1})=-(arcsin(x))^(-2)* 1/sqrt{1-x^2}

=-1/(arcsin^{2}(x)sqrt{1-x^2})

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