derivative of sqrt((x^3+14x-7/7))

Lösung

\frac{d}{d x} (\frac{x ^{3} + 14 x - 7}{7})

\frac{3 x ^{2} + 14}{2 7 x ^{3} + 14 x - 7}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{3} + 14 x - 7}{7})

Wende die Kettenregel an:

\frac{1}{2 \frac{x ^{3} + 14 x - 7}{7}} \frac{d}{d x} (\frac{x ^{3} + 14 x - 7}{7})

= \frac{1}{2 \frac{x ^{3} + 14 x - 7}{7}} \frac{d}{d x} (\frac{x ^{3} + 14 x - 7}{7})

\frac{d}{d x} (\frac{x ^{3} + 14 x - 7}{7}) = \frac{1}{7} (3 x^{2} + 14)

= \frac{1}{2 \frac{x ^{3} + 14 x - 7}{7}} \cdot \frac{1}{7} (3 x^{2} + 14)

Vereinfache

\frac{1}{2 \frac{x ^{3} + 14 x - 7}{7}} \cdot \frac{1}{7} (3 x^{2} + 14) : \frac{3 x ^{2} + 14}{2 7 x ^{3} + 14 x - 7}

= \frac{3 x ^{2} + 14}{2 7 x ^{3} + 14 x - 7}

\int \frac{ln ( x ^{21} )}{x} d x

\int_{- 2}^{1} (2 x + π) d x

\int \frac{2 + x}{x ^{3}} d x

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

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