implicit (dy)/(dx),2x^4+9y=2x^2y+36

Lösung

implizite ableitung

\frac{d y}{d x}, 2 x^{4} + 9 y = 2 x^{2} y + 36

\frac{d y}{d x} = \frac{4 x y - 8 x ^{3}}{9 - 2 x ^{2}}

Schritte zur Lösung

2 x^{4} + 9 y = 2 x^{2} y + 36

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

8 x^{3} + 9 \frac{d y}{d x} = 2 (x^{2} \frac{d y}{d x} + 2 x y)

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{4 x y - 8 x ^{3}}{9 - 2 x ^{2}}

\frac{d y}{d x} = \frac{4 x y - 8 x ^{3}}{9 - 2 x ^{2}}

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

in v erse l a pl a ce \frac{( s )}{s ^{2} + 5 s + 6}

\frac{d}{d x} (\frac{( - 2 x - 3 ) ^{7}}{( 4 x + 2 ) ^{4}})

\frac{d y}{d x} + 10 y = 8

\int_{1}^{5} x^{3} - 5 x^{2} - x + 5 d x