(\partial)/(\partial x)(y/x ln(x))

Lösung

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

\frac{y ( - ln ( x ) + 1 )}{x ^{2}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= y \frac{\partial}{\partial x} (\frac{1}{x} ln (x))

Wende die Produktregel an:

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

f = \frac{1}{x}, g = ln (x)

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

\frac{\partial}{\partial x} (\frac{1}{x}) = - \frac{1}{x ^{2}}

\frac{\partial}{\partial x} (ln (x)) = \frac{1}{x}

= y ((- \frac{1}{x ^{2}}) ln (x) + \frac{1}{x} \cdot \frac{1}{x})

Vereinfache

y ((- \frac{1}{x ^{2}}) ln (x) + \frac{1}{x} \cdot \frac{1}{x}) : \frac{y ( - ln ( x ) + 1 )}{x ^{2}}

= \frac{y ( - ln ( x ) + 1 )}{x ^{2}}

n = 1 \sum \infty (cos (2.6))^{n}

y^{^{''}} + 4 y = 3 cos (2 t)

\frac{d}{d n} (n^{n})

\frac{d r}{d θ} = \frac{r ^{2} + 2 r θ}{θ ^{2}}

x \to 1 lim (e^{x - 1} + 1)