What is the solution for derivative of f(x)=(x-sqrt(1-x^2))^2 ?

The solution for derivative of f(x)=(x-sqrt(1-x^2))^2 is f(x)= 2/3 (-x^2+1)^{3/2}+x+c_{1}

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derivative of f(x)=(x-sqrt(1-x^2))^2

\frac{d}{d x} f (x) = (x - 1 - x^{2})^{2}

f (x) = \frac{2}{3} (- x^{2} + 1)^{\frac{3}{2}} + x + c_{1}

Solution steps

\frac{df}{d x} = (x - 1 - x^{2})^{2}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

f (x) = \int (x - 1 - x^{2})^{2} d x

\int (x - 1 - x^{2})^{2} d x = \frac{2}{3} (- x^{2} + 1)^{\frac{3}{2}} + x + c_{1}

f (x) = \frac{2}{3} (- x^{2} + 1)^{\frac{3}{2}} + x + c_{1}

What is the solution for derivative of f(x)=(x-sqrt(1-x^2))^2 ?
The solution for derivative of f(x)=(x-sqrt(1-x^2))^2 is f(x)= 2/3 (-x^2+1)^{3/2}+x+c_{1}