implicit (dy)/(dx),4x^2y^7-2x=x^5+4y^3

Lösung

implizite ableitung

\frac{d y}{d x}, 4 x^{2} y^{7} - 2 x = x^{5} + 4 y^{3}

\frac{d y}{d x} = \frac{5 x ^{4} - 8 x y ^{7} + 2}{4 y ^{2} ( - 3 + 7 x ^{2} y ^{4} )}

Schritte zur Lösung

4 x^{2} y^{7} - 2 x = x^{5} + 4 y^{3}

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

4 (2 x y^{7} + 7 y^{6} \frac{d y}{d x} x^{2}) - 2 = 5 x^{4} + 12 y^{2} \frac{d y}{d x}

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{5 x ^{4} - 8 x y ^{7} + 2}{4 y ^{2} ( - 3 + 7 x ^{2} y ^{4} )}

\frac{d y}{d x} = \frac{5 x ^{4} - 8 x y ^{7} + 2}{4 y ^{2} ( - 3 + 7 x ^{2} y ^{4} )}

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

f (x) = e^{x} - 1

d er i v a t i v e f (x) = x^{3} - 4

\int (1 - x - y)^{2} d y

\int \frac{1}{4 y} d y