derivative of x(dy/(dx))

Lösung

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

\frac{d y}{d x} + x \frac{d ^{2} y}{d x ^{2}}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = \frac{d y}{d x}

= \frac{d x}{d x} \frac{d y}{d x} + \frac{d ^{2} y}{d x ^{2}} x

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

= 1 \frac{d y}{d x} + \frac{d ^{2} y}{d x ^{2}} x

Vereinfache

= \frac{d y}{d x} + x \frac{d ^{2} y}{d x ^{2}}

y^{^{'}} + 3 y = 2 e^{- 3 t}

d er i v a t i v e f (x) = \frac{( x - 2 )}{( 2 x ^{2} + 3 )}

\int_{2}^{3} \frac{1}{x ^{2} - 4 x} d x

d er i v a t i v e 3 x^{4} - 5 x + 2 3 x

\frac{d}{d x} (ln (1 - 6 x))