implicit (d^2y)/(dx^2),x^2+y^2=16

Lösung

implizite ableitung

\frac{d ^{2} y}{d x ^{2}}, x^{2} + y^{2} = 16

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

Schritte zur Lösung

x^{2} + y^{2} = 16

Behandle

y

wie

y (x)

Implizite Ableitung

\frac{d y}{d x}

von

x^{2} + y^{2} = 16 : - \frac{x}{y}

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

Implizite Ableitung

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

von

\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}}

Ersetze

\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}}

\frac{\partial}{\partial z} (x y + yz - x z)

1 - y^{2} d x = 1 - x^{2} d y

x \to 0 lim (\frac{- 2 e ^{- x}}{2 x - 2})

\int \frac{e ^{4 x}}{- 4 x} d x

x \to + 0 lim (\frac{( 3 e ^{x} - 3 )}{x})