derivative \sqrt[3]{3x^5+4x^4}

Lösung

ableitung von

3 3 x^{5} + 4 x^{4}

\frac{15 x ^{4} + 16 x ^{3}}{3 ( 3 x ^{5} + 4 x ^{4} ) ^{\frac{2}{3}}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (3 x^{5} + 4 x^{4}) = 15 x^{4} + 16 x^{3}

= \frac{1}{3 ( 3 x ^{5} + 4 x ^{4} ) ^{\frac{2}{3}}} (15 x^{4} + 16 x^{3})

Vereinfache

\frac{1}{3 ( 3 x ^{5} + 4 x ^{4} ) ^{\frac{2}{3}}} (15 x^{4} + 16 x^{3}) : \frac{15 x ^{4} + 16 x ^{3}}{3 ( 3 x ^{5} + 4 x ^{4} ) ^{\frac{2}{3}}}

= \frac{15 x ^{4} + 16 x ^{3}}{3 ( 3 x ^{5} + 4 x ^{4} ) ^{\frac{2}{3}}}

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

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

t an g e n t f (x) = 4 3 x, at x = 1

\int_{3}^{3} (x + 1) d x

d er i v a t i v e \frac{7}{5 x}