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Beliebt Rechnen >

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

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

Graph

Beliebte Beispiele

sum from n=1 to infinity of n/(2^n)

n = 1 \sum \infty \frac{n}{2 ^{n}}

slopeintercept (6,-1),(-3,-10)

s l o p e in t erce pt (6, - 1), (- 3, - 10)

d/(dy)((y^3)/(30)+5/(2y))

\frac{d}{d y} (\frac{y ^{3}}{30} + \frac{5}{2 y})

derivative (x^2+1)^3

d er i v a t i v e (x^{2} + 1)^{3}

tangent y= 2/(x-8)

t an g e n t y = \frac{2}{x - 8}