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Beliebt Rechnen >

derivative of 7/(3x^7-12x^6+2x^2-9)

Lösung

\frac{d}{d x} (\frac{7}{3 x ^{7} - 12 x ^{6} + 2 x ^{2} - 9})

Lösung

- \frac{7 ( 21 x ^{6} - 72 x ^{5} + 4 x )}{( 3 x ^{7} - 12 x ^{6} + 2 x ^{2} - 9 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{7}{3 x ^{7} - 12 x ^{6} + 2 x ^{2} - 9})

Entferne die Konstante:

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

= 7 \frac{d}{d x} (\frac{1}{3 x ^{7} - 12 x ^{6} + 2 x ^{2} - 9})

Wende Exponentenregel an:

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

= 7 \frac{d}{d x} ((3 x^{7} - 12 x^{6} + 2 x^{2} - 9)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 3 x ^{7} - 12 x ^{6} + 2 x ^{2} - 9 ) ^{2}} \frac{d}{d x} (3 x^{7} - 12 x^{6} + 2 x^{2} - 9)

= - \frac{1}{( 3 x ^{7} - 12 x ^{6} + 2 x ^{2} - 9 ) ^{2}} \frac{d}{d x} (3 x^{7} - 12 x^{6} + 2 x^{2} - 9)

\frac{d}{d x} (3 x^{7} - 12 x^{6} + 2 x^{2} - 9) = 21 x^{6} - 72 x^{5} + 4 x

= 7 (- \frac{1}{( 3 x ^{7} - 12 x ^{6} + 2 x ^{2} - 9 ) ^{2}} (21 x^{6} - 72 x^{5} + 4 x))

Vereinfache

7 (- \frac{1}{( 3 x ^{7} - 12 x ^{6} + 2 x ^{2} - 9 ) ^{2}} (21 x^{6} - 72 x^{5} + 4 x)) : - \frac{7 ( 21 x ^{6} - 72 x ^{5} + 4 x )}{( 3 x ^{7} - 12 x ^{6} + 2 x ^{2} - 9 ) ^{2}}

= - \frac{7 ( 21 x ^{6} - 72 x ^{5} + 4 x )}{( 3 x ^{7} - 12 x ^{6} + 2 x ^{2} - 9 ) ^{2}}

Graph

Beliebte Beispiele

tangent y= 1/(x+2),\at x=7

t an g e n t y = \frac{1}{x + 2}, at x = 7

limit as x approaches 8 of 9x+|x-8|

x \to 8 lim (9 x + ∣ x - 8 ∣)

tangent f(x)=x^2-1/x ,(1,0)

t an g e n t f (x) = x^{2} - \frac{1}{x}, (1, 0)

d/(d{x)}(1/(sqrt(9-{x)^2-{y)^2-{z}^2}})

\frac{d}{d x} (\frac{1}{9 - x ^{2} - y ^{2} - z ^{2}})

((x - 1)^{2})^{^{'}}