implicit (dy)/(dx),y-5xy^3+8=5sin(y^3+2x^2)

Lösung

implizite ableitung

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

\frac{d y}{d x} = \frac{20 x cos ( y ^{3} + 2 x ^{2} ) + 5 y ^{3}}{1 - 15 x y ^{2} - 15 y ^{2} cos ( y ^{3} + 2 x ^{2} )}

Schritte zur Lösung

y - 5 x y^{3} + 8 = 5 sin (y^{3} + 2 x^{2})

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

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

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{20 x cos ( y ^{3} + 2 x ^{2} ) + 5 y ^{3}}{1 - 15 x y ^{2} - 15 y ^{2} cos ( y ^{3} + 2 x ^{2} )}

\frac{d y}{d x} = \frac{20 x cos ( y ^{3} + 2 x ^{2} ) + 5 y ^{3}}{1 - 15 x y ^{2} - 15 y ^{2} cos ( y ^{3} + 2 x ^{2} )}

\frac{\partial}{\partial x} (x (y + 1))

\int_{0}^{2 π} sin^{4} (x) d x

\frac{d}{d x} (sin (9 x) + (sin (9 x))^{2})

d er i v a t i v e f (2 x) = 5 x - 3

\frac{\partial}{\partial x} (x + y)