derivative of (e^2/(x(3x-5)))

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

= e^{2} (- \frac{1}{( x ( 3 x - 5 ) ) ^{2}} (6 x - 5))

Vereinfache

e^{2} (- \frac{1}{( x ( 3 x - 5 ) ) ^{2}} (6 x - 5)) : - \frac{e ^{2} ( 6 x - 5 )}{x ^{2} ( 3 x - 5 ) ^{2}}

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

\int \frac{3 x ^{2} + 5 x + 3}{( x ^{2} + 1 ) ^{2}} d x

d er i v a t i v e f (x) = 5 x^{2} tan (1 - x)

d er i v a t i v e x (x^{2} + 7)^{4}

t an g e n t 2 x^{3} - 2 x^{2} + 1

x \to 7 + lim (\frac{3}{x - 7})