derivative of 3sin(x+sin(y))=2

Lösung

\frac{d}{d x} (3 sin (x) + sin (y)) = 2

y = arcsin (2 x + c_{1} - 3 sin (x)) + 2 πn, y = π + arcsin (- 2 x - c_{1} + 3 sin (x)) + 2 πn

Schritte zur Lösung

\frac{d}{d x} (3 sin (x) + sin (y)) = 2

Wenn

f^{^{'}} (x) = g (x)

dann

f (x) = \int g (x) d x

3 sin (x) + sin (y) = \int 2 d x

\int 2 d x = 2 x + c_{1}

3 sin (x) + sin (y) = 2 x + c_{1}

Isoliere

y : y = arcsin (2 x + c_{1} - 3 sin (x)) + 2 πn, y = π + arcsin (- 2 x - c_{1} + 3 sin (x)) + 2 πn

y = arcsin (2 x + c_{1} - 3 sin (x)) + 2 πn, y = π + arcsin (- 2 x - c_{1} + 3 sin (x)) + 2 πn

y^{^{'}} = \frac{12 ln ^{3} ( x )}{x e ^{y}}

y^{2} + y = (x^{2} - x) y^{^{'}}

x y^{^{'}} - y = 3

(5 + y) y^{^{'}} = sin (7 + x)

y^{^{'}} + 6 e^{x + y} = 0