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Beliebt Rechnen >

derivative y= 1/(sqrt(a^2-x^2))

Lösung

ableitung von

y = \frac{1}{a ^{2} - x ^{2}}

Lösung

\frac{x}{( a ^{2} - x ^{2} ) ^{\frac{3}{2}}}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

(\partial)/(\partial x)(e^{x/(b(x))})

\frac{\partial}{\partial x} (e^{\frac{x}{b ( x )}})

limit as t approaches 0 of 5/(1+t)

t \to 0 lim (\frac{5}{1 + t})

y^{''}-3y^'=18t+26sin(2t)

y^{^{''}} - 3 y^{^{'}} = 18 t + 26 sin (2 t)

y^{''}+16y=32sin(4t)

y^{^{''}} + 16 y = 32 sin (4 t)

derivative of 2/3 x+4/(3x^2)

\frac{d}{d x} (\frac{2}{3} x + \frac{4}{3 x ^{2}})