derivative of 7/(x^8+5x+1)

Lösung

\frac{d}{d x} (\frac{7}{x ^{8} + 5 x + 1})

- \frac{7 ( 8 x ^{7} + 5 )}{( x ^{8} + 5 x + 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{7}{x ^{8} + 5 x + 1})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 7 \frac{d}{d x} (\frac{1}{x ^{8} + 5 x + 1})

Wende Exponentenregel an:

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

= 7 \frac{d}{d x} ((x^{8} + 5 x + 1)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( x ^{8} + 5 x + 1 ) ^{2}} \frac{d}{d x} (x^{8} + 5 x + 1)

= - \frac{1}{( x ^{8} + 5 x + 1 ) ^{2}} \frac{d}{d x} (x^{8} + 5 x + 1)

\frac{d}{d x} (x^{8} + 5 x + 1) = 8 x^{7} + 5

= 7 (- \frac{1}{( x ^{8} + 5 x + 1 ) ^{2}} (8 x^{7} + 5))

Vereinfache

7 (- \frac{1}{( x ^{8} + 5 x + 1 ) ^{2}} (8 x^{7} + 5)) : - \frac{7 ( 8 x ^{7} + 5 )}{( x ^{8} + 5 x + 1 ) ^{2}}

= - \frac{7 ( 8 x ^{7} + 5 )}{( x ^{8} + 5 x + 1 ) ^{2}}

\frac{d}{d x} (sin (14 x))

y^{^{'}} = 1 + y^{2} + x + x y^{2}

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

x \to 0 lim (2 x + 12)

y^{^{''}} + 16 y = 2 sec (4 x)