implicit (d^2y)/(dx^2),xy+7ey(x)=7e

Lösung

implizite ableitung

\frac{d ^{2} y}{d x ^{2}}, x y + 7 ey (x) = 7 e

\frac{d ^{2} y}{d x ^{2}} = \frac{2 y}{( x + 7 e ) ^{2}}

Schritte zur Lösung

x y + 7 ey = 7 e

Behandle

y

wie

y (x)

Implizite Ableitung

\frac{d y}{d x}

von

x y + 7 ey = 7 e : - \frac{y}{x + 7 e}

\frac{d y}{d x} = - \frac{y}{x + 7 e}

Implizite Ableitung

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

von

\frac{d y}{d x} = - \frac{y}{x + 7 e} : - \frac{\frac{d y}{d x} ( x + 7 e ) - y}{( x + 7 e ) ^{2}}

\frac{d ^{2} y}{d x ^{2}} = - \frac{\frac{d y}{d x} ( x + 7 e ) - y}{( x + 7 e ) ^{2}}

Ersetze

\frac{d y}{d x} = - \frac{y}{x + 7 e} : \frac{2 y}{( x + 7 e ) ^{2}}

\frac{d ^{2} y}{d x ^{2}} = \frac{2 y}{( x + 7 e ) ^{2}}

\frac{d}{d x} (\frac{2 x cos ( x ^{2} )}{sin ( x ^{2} ) + 1})

\int \frac{x}{x ^{2} - 16} d x

(x + y) \frac{d y}{d x} = 1

a re a - x^{2} + 9, - 2 x^{2} + 18

x \to 28.3 lim (f (x))