derivative of 1/(6x-7)

Lösung

\frac{d}{d x} (\frac{1}{6 x - 7})

- \frac{6}{( 6 x - 7 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{6 x - 7})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((6 x - 7)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 6 x - 7 ) ^{2}} \frac{d}{d x} (6 x - 7)

= - \frac{1}{( 6 x - 7 ) ^{2}} \frac{d}{d x} (6 x - 7)

\frac{d}{d x} (6 x - 7) = 6

= - \frac{1}{( 6 x - 7 ) ^{2}} \cdot 6

Vereinfache

- \frac{1}{( 6 x - 7 ) ^{2}} \cdot 6 : - \frac{6}{( 6 x - 7 ) ^{2}}

= - \frac{6}{( 6 x - 7 ) ^{2}}

x \to - 1 lim (3 x^{2} - 3 x + 3)

\frac{d}{d x} ((- 1)^{n} x^{n})

\int \frac{1}{x ^{4}} - \frac{1}{4 x} + 4 d x

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

y^{^{''}} + 2 y^{^{'}} - 3 y = 0, y (0) = 4, y^{^{'}} (0) = 1