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Beliebt Rechnen >

derivative of 1/((25-x^2))

Lösung

\frac{d}{d x} (\frac{1}{( 25 - x ^{2} )})

Lösung

\frac{2 x}{( 25 - x ^{2} ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{( 25 - x ^{2} )})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((25 - x^{2})^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 25 - x ^{2} ) ^{2}} \frac{d}{d x} (25 - x^{2})

= - \frac{1}{( 25 - x ^{2} ) ^{2}} \frac{d}{d x} (25 - x^{2})

\frac{d}{d x} (25 - x^{2}) = - 2 x

= - \frac{1}{( 25 - x ^{2} ) ^{2}} (- 2 x)

Vereinfache

- \frac{1}{( 25 - x ^{2} ) ^{2}} (- 2 x) : \frac{2 x}{( 25 - x ^{2} ) ^{2}}

= \frac{2 x}{( 25 - x ^{2} ) ^{2}}

Graph

Beliebte Beispiele

integral of e^7

\int e^{7} d x

y^{''}-2y^'-3y=3te^{2t},y(0)=1,y^'(0)=0

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 t e^{2 t}, y (0) = 1, y^{^{'}} (0) = 0

y^'=8x+y,y(0)=1

y^{^{'}} = 8 x + y, y (0) = 1

(dy)/(dx)=(2xy-y^2)/(x^2)

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

(dy)/(dx)=(4x^3)/(cos(y))

\frac{d y}{d x} = \frac{4 x ^{3}}{cos ( y )}