derivative ln(4x^3+5x^2+2x+5)

Lösung

ableitung von

ln (4 x^{3} + 5 x^{2} + 2 x + 5)

\frac{12 x ^{2} + 10 x + 2}{4 x ^{3} + 5 x ^{2} + 2 x + 5}

Schritte zur Lösung

\frac{d}{d x} (ln (4 x^{3} + 5 x^{2} + 2 x + 5))

Wende die Kettenregel an:

\frac{1}{4 x ^{3} + 5 x ^{2} + 2 x + 5} \frac{d}{d x} (4 x^{3} + 5 x^{2} + 2 x + 5)

= \frac{1}{4 x ^{3} + 5 x ^{2} + 2 x + 5} \frac{d}{d x} (4 x^{3} + 5 x^{2} + 2 x + 5)

\frac{d}{d x} (4 x^{3} + 5 x^{2} + 2 x + 5) = 12 x^{2} + 10 x + 2

= \frac{1}{4 x ^{3} + 5 x ^{2} + 2 x + 5} (12 x^{2} + 10 x + 2)

Vereinfache

\frac{1}{4 x ^{3} + 5 x ^{2} + 2 x + 5} (12 x^{2} + 10 x + 2) : \frac{12 x ^{2} + 10 x + 2}{4 x ^{3} + 5 x ^{2} + 2 x + 5}

= \frac{12 x ^{2} + 10 x + 2}{4 x ^{3} + 5 x ^{2} + 2 x + 5}

a re a y = 5 - x^{2}, y = 17 - 7 x

\int \frac{x + 5}{x ^{2} + 16} d x

d er i v a t i v e f (x) = \frac{( x ^{2} + 3 )}{x}

s l o p e in t erce pt (- 1, 1), (- 2, - 1)

d er i v a t i v e y = x + 5