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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (e^{- 2 x + x^{2}})

\int_{0}^{2} x - x d x

in v erse l a pl a ce \frac{s}{( s ^{2} + 4 s + 5 )}

a re a 4 - x^{2}, - 2, 2

\int (x - 3) cos (x) d x