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

Lösung

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

4 ln (2) x + 3

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (3 x) = 3

\frac{d}{d x} (3) = 0

= 4 ln (2) x + 3 + 0

Vereinfache

= 4 ln (2) x + 3

\int (6 sin (x) + 3 sinh (x)) d x

\int \frac{2 x + 1}{x ^{2} + 1} d x

\int \frac{x}{x ^{2} + 4 x + 8} d x

\int_{- 2}^{2} ∣ x ∣ d x

in v erse l a pl a ce \frac{6}{s ( 2 s ^{2} + 7 s + 3 )}