What is implicit (d^2y)/(dx^2),x^2+y^2=36 ?

The answer to implicit (d^2y)/(dx^2),x^2+y^2=36 is (d^2y)/(dx^2)=-(y^2+x^2)/(y^3)

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implicit (d^2y)/(dx^2),x^2+y^2=36

implicit derivative

\frac{d ^{2} y}{d x ^{2}}, x^{2} + y^{2} = 36

\frac{d ^{2} y}{d x ^{2}} = - \frac{y ^{2} + x ^{2}}{y ^{3}}

Solution steps

x^{2} + y^{2} = 36

Treat

y

y (x)

Implicit Derivative

\frac{d y}{d x}

x^{2} + y^{2} = 36 : - \frac{x}{y}

\frac{d y}{d x} = - \frac{x}{y}

Implicit Derivative

\frac{d ^{2} y}{d x ^{2}}

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

\frac{d ^{2} y}{d x ^{2}} = - \frac{y - x \frac{d y}{d x}}{y ^{2}}

Substitute

\frac{d y}{d x} = - \frac{x}{y} : - \frac{y ^{2} + x ^{2}}{y ^{3}}

\frac{d ^{2} y}{d x ^{2}} = - \frac{y ^{2} + x ^{2}}{y ^{3}}

What is implicit (d^2y)/(dx^2),x^2+y^2=36 ?
The answer to implicit (d^2y)/(dx^2),x^2+y^2=36 is (d^2y)/(dx^2)=-(y^2+x^2)/(y^3)