implicit (dy)/(dx),25x^2-10xy+4y^2=100

Lösung

implizite ableitung

\frac{d y}{d x}, 25 x^{2} - 10 x y + 4 y^{2} = 100

\frac{d y}{d x} = \frac{5 ( y - 5 x )}{4 y - 5 x}

Schritte zur Lösung

25 x^{2} - 10 x y + 4 y^{2} = 100

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

50 x - 10 (y + x \frac{d y}{d x}) + 8 y \frac{d y}{d x} = 0

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{5 ( y - 5 x )}{4 y - 5 x}

\frac{d y}{d x} = \frac{5 ( y - 5 x )}{4 y - 5 x}

\int \frac{( x ^{3} )}{9 - x ^{2}} d x

\frac{d ^{2}}{d x ^{2}} (x^{e^{x}})

d er i v a t i v e h (x) = \frac{( 3 x - 5 )}{1 - x ^{2}}

\frac{d}{d x} (3 x^{2})

\frac{d}{d x} (2 x^{3} + \frac{5 x + 1}{3 x - 5} - \frac{2}{x ^{3}})