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Beliebt Rechnen >

derivative f(x)= 6/(ln(x^2+4))

Lösung

ableitung von

f (x) = \frac{6}{ln ( x ^{2} + 4 )}

Lösung

- \frac{12 x}{ln ^{2} ( x ^{2} + 4 ) ( x ^{2} + 4 )}

Schritte zur Lösung

\frac{d}{d x} (\frac{6}{ln ( x ^{2} + 4 )})

Entferne die Konstante:

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

= 6 \frac{d}{d x} (\frac{1}{ln ( x ^{2} + 4 )})

Wende Exponentenregel an:

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

= 6 \frac{d}{d x} (ln^{- 1} (x^{2} + 4))

Wende die Kettenregel an:

- \frac{1}{( ln ( x ^{2} + 4 ) ) ^{2}} \frac{d}{d x} (ln (x^{2} + 4))

= - \frac{1}{( ln ( x ^{2} + 4 ) ) ^{2}} \frac{d}{d x} (ln (x^{2} + 4))

\frac{d}{d x} (ln (x^{2} + 4)) = \frac{2 x}{x ^{2} + 4}

= 6 (- \frac{1}{( ln ( x ^{2} + 4 ) ) ^{2}} \cdot \frac{2 x}{x ^{2} + 4})

Vereinfache

6 (- \frac{1}{ln ^{2} ( x ^{2} + 4 )} \cdot \frac{2 x}{x ^{2} + 4}) : - \frac{12 x}{ln ^{2} ( x ^{2} + 4 ) ( x ^{2} + 4 )}

= - \frac{12 x}{ln ^{2} ( x ^{2} + 4 ) ( x ^{2} + 4 )}

Graph

Beliebte Beispiele

integral of (sin(44x))/(1+cos^2(44x))

\int \frac{sin ( 44 x )}{1 + cos ^{2} ( 44 x )} d x

integral of 2x(x^2+1)^{-7}

\int 2 x (x^{2} + 1)^{- 7} d x

fläche f(x)=x^2,[0,3]

a re a f (x) = x^{2}, [0, 3]

integral from-1 to 3 of (x^2+6x+3)

\int_{- 1}^{3} (x^{2} + 6 x + 3) d x

(d^3)/(dx^3)(x^4-10x^3)

\frac{d ^{3}}{d x ^{3}} (x^{4} - 10 x^{3})