derivative f(x)= 1/(x^2+1)

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

l in e (1, 7), (- 2, 3)

\frac{d y}{d x} x^{2} - y^{2} = 16

θ = \frac{5 π}{4}

d er i v a t i v e f (x) = \frac{3}{2} x - 5

n or ma l f (x) = x^{2} + 2, at x = 2