derivative of ((x^3-1/(x^3+1))^8)

Lösung

\frac{d}{d x} ((\frac{x ^{3} - 1}{x ^{3} + 1})^{8})

\frac{48 x ^{2} ( x ^{3} - 1 ) ^{7}}{( x ^{3} + 1 ) ^{9}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{x ^{3} - 1}{x ^{3} + 1})^{8})

Wende die Kettenregel an:

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

= 8 (\frac{x ^{3} - 1}{x ^{3} + 1})^{7} \frac{d}{d x} (\frac{x ^{3} - 1}{x ^{3} + 1})

\frac{d}{d x} (\frac{x ^{3} - 1}{x ^{3} + 1}) = \frac{6 x ^{2}}{( x ^{3} + 1 ) ^{2}}

= 8 (\frac{x ^{3} - 1}{x ^{3} + 1})^{7} \frac{6 x ^{2}}{( x ^{3} + 1 ) ^{2}}

Vereinfache

8 (\frac{x ^{3} - 1}{x ^{3} + 1})^{7} \frac{6 x ^{2}}{( x ^{3} + 1 ) ^{2}} : \frac{48 x ^{2} ( x ^{3} - 1 ) ^{7}}{( x ^{3} + 1 ) ^{9}}

= \frac{48 x ^{2} ( x ^{3} - 1 ) ^{7}}{( x ^{3} + 1 ) ^{9}}

f (x) = sin^{3} (3 x)

f (t) = cos (2 t)

\frac{d}{d x} (2 \cdot cos (x))

\frac{d ^{3}}{d x ^{3}} (2 sin (2 x))

\int x^{3} ln (x^{4}) d x