implicit (dy)/(dx),8x^3+x^2y-xy^3=9

Lösung

implizite ableitung

\frac{d y}{d x}, 8 x^{3} + x^{2} y - x y^{3} = 9

\frac{d y}{d x} = \frac{- 24 x ^{2} - 2 x y + y ^{3}}{x ( x - 3 y ^{2} )}

Schritte zur Lösung

8 x^{3} + x^{2} y - x y^{3} = 9

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

24 x^{2} + 2 x y + x^{2} \frac{d y}{d x} - y^{3} - 3 x y^{2} \frac{d y}{d x} = 0

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- 24 x ^{2} - 2 x y + y ^{3}}{x ( x - 3 y ^{2} )}

\frac{d y}{d x} = \frac{- 24 x ^{2} - 2 x y + y ^{3}}{x ( x - 3 y ^{2} )}

\int \frac{1}{x ^{\frac{4}{5}} ( 1 + x ^{\frac{1}{5}} )} d x

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

t an g e n t f (x) = 7 x + 32, at x = - 1

(x + y) d x + (x + y - 1) d y = 0

\int (\frac{- y}{x ^{2} + y ^{2}}) d x