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Beliebt Rechnen >

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

Lösung

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

Lösung

\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}

Beliebte Beispiele

5 y^{^{'}} - 15 x^{2} = 0

limit as n approaches 10 of [1+(1/n)]^n

n \to 10 lim ([1 + (\frac{1}{n})]^{n})

derivative of 2(1-x^{-3})

\frac{d}{d x} (2 (1 - x)^{- 3})

limit as x approaches 0 of (5^x-4^x)/x

x \to 0 lim (\frac{5 ^{x} - 4 ^{x}}{x})

derivative (2x+3)/(3x+2)

d er i v a t i v e \frac{2 x + 3}{3 x + 2}