derivative y=(2log_{e}(x)-3)^4

Lösung

ableitung von

y = (2 lo g_{e} (x) - 3)^{4}

\frac{8 ( 2 ln ( x ) - 3 ) ^{3}}{x}

Schritte zur Lösung

\frac{d}{d x} ((2 lo g_{e} (x) - 3)^{4})

Vereinfache

(2 lo g_{e} (x) - 3)^{4} : (2 ln (x) - 3)^{4}

= \frac{d}{d x} ((2 ln (x) - 3)^{4})

Wende die Kettenregel an:

4 (2 ln (x) - 3)^{3} \frac{d}{d x} (2 ln (x) - 3)

= 4 (2 ln (x) - 3)^{3} \frac{d}{d x} (2 ln (x) - 3)

\frac{d}{d x} (2 ln (x) - 3) = \frac{2}{x}

= 4 (2 ln (x) - 3)^{3} \frac{2}{x}

Vereinfache

4 (2 ln (x) - 3)^{3} \frac{2}{x} : \frac{8 ( 2 ln ( x ) - 3 ) ^{3}}{x}

= \frac{8 ( 2 ln ( x ) - 3 ) ^{3}}{x}

\int \frac{( 7 x + 29 )}{x ^{2} + 8 x + 15} d x

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

d er i v a t i v e 1 + x^{3}

x \to 0 lim (2 x - \frac{1}{x ^{2}})

in v erse l a pl a ce \frac{1}{( s - 2 ) ( s + 1 ) ( s - 3 )}