derivative of 1/(x^2-25)

Lösung

\frac{d}{d x} (\frac{1}{x ^{2} - 25})

- \frac{2 x}{( x ^{2} - 25 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{x ^{2} - 25})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((x^{2} - 25)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( x ^{2} - 25 ) ^{2}} \frac{d}{d x} (x^{2} - 25)

= - \frac{1}{( x ^{2} - 25 ) ^{2}} \frac{d}{d x} (x^{2} - 25)

\frac{d}{d x} (x^{2} - 25) = 2 x

= - \frac{1}{( x ^{2} - 25 ) ^{2}} \cdot 2 x

Vereinfache

- \frac{1}{( x ^{2} - 25 ) ^{2}} \cdot 2 x : - \frac{2 x}{( x ^{2} - 25 ) ^{2}}

= - \frac{2 x}{( x ^{2} - 25 ) ^{2}}

y^{^{''}} + 25 y = sin (5 x)

\int sec^{2} (x) + 9 d x

\int - \frac{5 ^{- x}}{ln ( 5 )} d x

\int - 36 x^{2} - 18 x - 4 d x

y^{^{''}} + 2 y^{^{'}} - 8 y = 2 e^{- 3 x} - e^{- x}