derivative of (x^4+3x^{-1})

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

in v erse l a pl a ce \frac{s - 1}{( s + 1 ) ( s + 2 ) s}

f (x) = \frac{5}{x ^{5}}

t a y l or f (x) = sin (x), 0

a re a x^{2} + x + 3, [1, 3]

\int \frac{2}{3} cos^{2} (3 x) d x