derivative f(x)=ln(x^3+5x+3)

Lösung

ableitung von

f (x) = ln (x^{3} + 5 x + 3)

\frac{3 x ^{2} + 5}{x ^{3} + 5 x + 3}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{3 x ^{2} + 5}{x ^{3} + 5 x + 3}

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

d er i v a t i v e y = - \frac{4}{5 x ^{5}} + \frac{15}{4 x ^{4}}

d er i v a t i v e f (x) = x^{2} + 21

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

\frac{d}{d x} (x^{2} 2^{x})