derivative of yx

Lösung

\frac{d}{d x} (y x)

x \frac{d y}{d x} + y

Schritte zur Lösung

\frac{d}{d x} (y x)

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = x

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

\frac{d x}{d x} = 1

= \frac{d y}{d x} x + 1 \cdot y

Vereinfache

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

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = 0

t an g e n t y = \frac{- 6 x}{x ^{2} + 1}, (1, - 3)

y^{^{'}} = y (1 - 0.001 y)

\int_{0}^{1} π (x^{2})^{2} d x

\frac{d}{d t} (6 t)