(\partial)/(\partial x)(sqrt(x)*ln(t))

Lösung

\frac{\partial}{\partial x} (x \cdot ln (t))

\frac{ln ( t )}{2 x}

Schritte zur Lösung

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

Behandle

t

als Konstante

Entferne die Konstante:

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

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

Wende Radikal Regel an:

a = a^{\frac{1}{2}}

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

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Vereinfache

ln (t) \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{ln ( t )}{2 x}

= \frac{ln ( t )}{2 x}

\frac{d v}{d t} = 9.81 - \frac{0.5}{v ^{- 1}}

k = 0 \sum \infty 5 \cdot 3^{k}

d er i v a t i v e - \frac{4 x}{( x ^{2} - 1 ) ^{2}}

x \to 0 + lim (x^{2} - 2 x - 3)

\frac{\partial}{\partial x} (2 + y ln (4 + x y^{2}))