derivative f(x)= 3/((x^2-5x)^2)

Lösung

ableitung von

f (x) = \frac{3}{( x ^{2} - 5 x ) ^{2}}

- \frac{6 ( 2 x - 5 )}{( x ^{2} - 5 x ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3}{( x ^{2} - 5 x ) ^{2}})

Entferne die Konstante:

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

= 3 \frac{d}{d x} (\frac{1}{( x ^{2} - 5 x ) ^{2}})

Wende Exponentenregel an:

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

= 3 \frac{d}{d x} ((x^{2} - 5 x)^{- 2})

Wende die Kettenregel an:

- \frac{2}{( x ^{2} - 5 x ) ^{3}} \frac{d}{d x} (x^{2} - 5 x)

= - \frac{2}{( x ^{2} - 5 x ) ^{3}} \frac{d}{d x} (x^{2} - 5 x)

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

= 3 (- \frac{2}{( x ^{2} - 5 x ) ^{3}} (2 x - 5))

Vereinfache

3 (- \frac{2}{( x ^{2} - 5 x ) ^{3}} (2 x - 5)) : - \frac{6 ( 2 x - 5 )}{( x ^{2} - 5 x ) ^{3}}

= - \frac{6 ( 2 x - 5 )}{( x ^{2} - 5 x ) ^{3}}

d er i v a t i v e y = 1 cos (2) (x)

t a y l or e^{t^{2}}

\int e^{x} sec^{2} (e^{x}) d x

y^{^{''}} + 25 y = 20 sin (5 x)

e^{x - y} d x + e^{y - x} d y = 0