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Beliebt Rechnen >

derivative of (4+x^2^{-1})

Lösung

\frac{d}{d x} ((4 + x^{2})^{- 1})

Lösung

- \frac{2 x}{( 4 + x ^{2} ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} ((4 + x^{2})^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 4 + x ^{2} ) ^{2}} \frac{d}{d x} (4 + x^{2})

= - \frac{1}{( 4 + x ^{2} ) ^{2}} \frac{d}{d x} (4 + x^{2})

\frac{d}{d x} (4 + x^{2}) = 2 x

= - \frac{1}{( 4 + x ^{2} ) ^{2}} \cdot 2 x

Vereinfache

- \frac{1}{( 4 + x ^{2} ) ^{2}} \cdot 2 x : - \frac{2 x}{( 4 + x ^{2} ) ^{2}}

= - \frac{2 x}{( 4 + x ^{2} ) ^{2}}

Graph

Beliebte Beispiele

integral of (x^8-(2x^5)/7-sqrt(5))

\int (x^{8} - \frac{2 x ^{5}}{7} - 5) d x

y^'=(x^2+xy+y^2)/(x^2)

y^{^{'}} = \frac{x ^{2} + x y + y ^{2}}{x ^{2}}

d y = (x - 2 x y) d x

tangent x^2+4x-8

t an g e n t x^{2} + 4 x - 8

limit as x approaches 0+of x^5ln(x)

x \to 0 + lim (x^{5} ln (x))