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Beliebt Rechnen >

derivative of xsqrt(a^2-x^2)

Lösung

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

Lösung

\frac{- 2 x ^{2} + a ^{2}}{a ^{2} - x ^{2}}

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = a^{2} - x^{2}

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

\frac{d x}{d x} = 1

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

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

Vereinfache

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

= \frac{- 2 x ^{2} + a ^{2}}{a ^{2} - x ^{2}}

Graph

Beliebte Beispiele

derivative of 1/(2sqrt(x)+1/(9x^{8/9)})

\frac{d}{d x} (\frac{1}{2 x} + \frac{1}{9 x ^{\frac{8}{9}}})

integral from 1 to 2 of (sqrt(x-1))/x

\int_{1}^{2} \frac{x - 1}{x} d x

integral of e^x*2x

\int e^{x} \cdot 2 x d x

derivative w/(w+c/w)

d er i v a t i v e \frac{w}{w + \frac{c}{w}}

tangent y=x^2-6,\at x=a

t an g e n t y = x^{2} - 6, at x = a