What is derivative of x=(1-y^2)^{1/2} ?

The answer to derivative of x=(1-y^2)^{1/2} is (dy}{dx}=-\frac{(1-y^2)^{1/2})/y

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derivative of x=(1-y^2)^{1/2}

derivative of

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

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

Solution steps

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

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

2 x^{2} + 2 y - 2 x y = 4

x^{2} + 2 x y = y^{2}

x^{3} + x^{2} y + 7 x y^{2} + y^{3} = 81

y - 4 = 2 (x - 1)^{2}

y^{2} x^{3} + x^{2} + y = 7

What is derivative of x=(1-y^2)^{1/2} ?
The answer to derivative of x=(1-y^2)^{1/2} is (dy}{dx}=-\frac{(1-y^2)^{1/2})/y