derivative of log_{5}(x^4sqrt(2x^2+9x))

Lösung

\frac{d}{d x} (lo g_{5} (x^{4} 2 x^{2} + 9 x))

\frac{20 x + 81}{2 ln ( 5 ) x ( 2 x + 9 )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{5} (x^{4} 2 x^{2} + 9 x))

Wende die log Regel an:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( x ^{4} 2 x ^{2} + 9 x )}{ln ( 5 )})

Entferne die Konstante:

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

= \frac{1}{ln ( 5 )} \frac{d}{d x} (ln (x^{4} 2 x^{2} + 9 x))

Wende die Kettenregel an:

\frac{1}{x ^{4} 2 x ^{2} + 9 x} \frac{d}{d x} (x^{4} 2 x^{2} + 9 x)

= \frac{1}{x ^{4} 2 x ^{2} + 9 x} \frac{d}{d x} (x^{4} 2 x^{2} + 9 x)

\frac{d}{d x} (x^{4} 2 x^{2} + 9 x) = \frac{20 x ^{5} + 81 x ^{4}}{2 2 x ^{2} + 9 x}

= \frac{1}{ln ( 5 )} \cdot \frac{1}{x ^{4} 2 x ^{2} + 9 x} \cdot \frac{20 x ^{5} + 81 x ^{4}}{2 2 x ^{2} + 9 x}

Vereinfache

\frac{1}{ln ( 5 )} \cdot \frac{1}{x ^{4} 2 x ^{2} + 9 x} \cdot \frac{20 x ^{5} + 81 x ^{4}}{2 2 x ^{2} + 9 x} : \frac{20 x + 81}{2 ln ( 5 ) x ( 2 x + 9 )}

= \frac{20 x + 81}{2 ln ( 5 ) x ( 2 x + 9 )}

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

x y^{^{'}} = y + x e^{\frac{y}{x}}

\int_{- 4}^{2} - x^{2} - 2 x + 8 d x

t an g e n t y = sin (7 x) + sin^{2} (7 x), (0, 0)

\int_{0}^{1} ∣ 2 x - 1 ∣ d x