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Beliebt Rechnen >

derivative of 2xlog_{6}(sqrt(x))

Lösung

\frac{d}{d x} (2 x lo g_{6} (x))

Lösung

lo g_{6} (x) + \frac{1}{ln ( 6 )}

Schritte zur Lösung

\frac{d}{d x} (2 x lo g_{6} (x))

Entferne die Konstante:

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

= 2 \frac{d}{d x} (x lo g_{6} (x))

Wende die Produktregel an:

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

f = x, g = lo g_{6} (x)

= 2 (\frac{d x}{d x} lo g_{6} (x) + \frac{d}{d x} (lo g_{6} (x)) x)

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

\frac{d}{d x} (lo g_{6} (x)) = \frac{1}{2 ln ( 6 ) x}

= 2 (1 \cdot lo g_{6} (x) + \frac{1}{2 ln ( 6 ) x} x)

Vereinfache

2 (1 \cdot lo g_{6} (x) + \frac{1}{2 ln ( 6 ) x} x) : lo g_{6} (x) + \frac{1}{ln ( 6 )}

= lo g_{6} (x) + \frac{1}{ln ( 6 )}

Graph

Beliebte Beispiele

integral of sin(2x+5)

\int sin (2 x + 5) d x

normal y=sqrt(x),\at x=4

n or ma l y = x, at x = 4

integral of (7x+6)/(x^2(x+2))

\int \frac{7 x + 6}{x ^{2} ( x + 2 )} d x

(\partial)/(\partial t)(t^2e^{-x})

\frac{\partial}{\partial t} (t^{2} e^{- x})

derivative of sqrt(1-5x)

\frac{d}{d x} (1 - 5 x)