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Beliebt Rechnen >

derivative F(x)= 3/(1+x^2)

Lösung

ableitung von

F (x) = \frac{3}{1 + x ^{2}}

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

= 3 (- \frac{1}{( 1 + x ^{2} ) ^{2}} \cdot 2 x)

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of sqrt(3x-5)

\int 3 x - 5 d x

(\partial)/(\partial z)(x^2y)

\frac{\partial}{\partial z} (x^{2} y)

limit as x approaches pi of+(ln(sin(x)))

x \to π lim (+ (ln (sin (x))))

(\partial)/(\partial x)(x/(x^5-y^3))

\frac{\partial}{\partial x} (\frac{x}{x ^{5} - y ^{3}})

derivative of-2x-1

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