derivative 1/(5x^2+6x)

Lösung

ableitung von

\frac{1}{5 x ^{2} + 6 x}

- \frac{10 x + 6}{( 5 x ^{2} + 6 x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{5 x ^{2} + 6 x})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((5 x^{2} + 6 x)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 5 x ^{2} + 6 x ) ^{2}} \frac{d}{d x} (5 x^{2} + 6 x)

= - \frac{1}{( 5 x ^{2} + 6 x ) ^{2}} \frac{d}{d x} (5 x^{2} + 6 x)

\frac{d}{d x} (5 x^{2} + 6 x) = 10 x + 6

= - \frac{1}{( 5 x ^{2} + 6 x ) ^{2}} (10 x + 6)

Vereinfache

- \frac{1}{( 5 x ^{2} + 6 x ) ^{2}} (10 x + 6) : - \frac{10 x + 6}{( 5 x ^{2} + 6 x ) ^{2}}

= - \frac{10 x + 6}{( 5 x ^{2} + 6 x ) ^{2}}

\frac{\partial}{\partial x} (16 3 y + 2 x)

x \to 0 lim (\frac{3 cos ( x )}{x})

\frac{d}{d x} (\frac{1 - sec ( x )}{tan ( x )})

im pl i c i t \frac{d y}{d x}, y = x^{3} + 7

\frac{d}{d x} (- x^{3})