implicit x/y+y/x =3piab^2

Lösung

implizite ableitung

\frac{x}{y} + \frac{y}{x} = 3 πa b^{2}

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

Schritte zur Lösung

\frac{x}{y} + \frac{y}{x} = 3 πa b^{2}

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

\frac{y - x \frac{d y}{d x}}{y ^{2}} + \frac{x \frac{d y}{d x} - y}{x ^{2}} = 0

Isoliere

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

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

in v erse l a pl a ce \frac{( - 2 s - 1 )}{s + 1}

\int \frac{1}{y ^{2} + x ^{2}} d x

s l o p e 2 x - 1, at x = 5

\int \frac{3 x ^{3} - 3 x + 4}{4 x ^{2} - 4} d x

\frac{d}{d x} (e^{x^{\frac{1}{3}}} + (e^{x})^{\frac{1}{3}})