derivative of 1/(1+x^4)

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (4 sec (x) - 8 cos (x))

a re a y = x^{3}, y = x, x \geq 0

\int_{0}^{1} x^{9} e^{x^{5}} d x

x \to 0 lim (\frac{( ln ( cos ( 2 x ) ) )}{x ^{2}})

x^{2} y^{^{''}} + 9 x y^{^{'}} - 20 y = \frac{5}{x ^{3}}