(\partial)/(\partial x)(1+ln(x)+y/x)

Lösung

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

\frac{1}{x} - \frac{y}{x ^{2}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (1) = 0

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

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

= 0 + \frac{1}{x} - \frac{y}{x ^{2}}

Vereinfache

= \frac{1}{x} - \frac{y}{x ^{2}}

x \to \infty lim (\frac{ln ( x )}{3 x})

ma c l a u r in \frac{1}{x - 1}

\frac{\partial}{\partial x} (x^{4} + y^{4} - 4 x + 1 y)

t an g e n t f (x) = 5 x^{\frac{1}{2}} + x^{\frac{3}{2}}, at x = 4

im pl i c i t \frac{d y}{d x}, y^{3} + y = x