derivative y=x^2sqrt(9-x^2)

Lösung

ableitung von

y = x^{2} 9 - x^{2}

\frac{- 3 x ^{3} + 18 x}{9 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (x^{2} 9 - x^{2})

Wende die Produktregel an:

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

f = x^{2}, g = 9 - x^{2}

= \frac{d}{d x} (x^{2}) 9 - x^{2} + \frac{d}{d x} (9 - x^{2}) x^{2}

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

\frac{d}{d x} (9 - x^{2}) = - \frac{x}{9 - x ^{2}}

= 2 x 9 - x^{2} + (- \frac{x}{9 - x ^{2}}) x^{2}

Vereinfache

2 x 9 - x^{2} + (- \frac{x}{9 - x ^{2}}) x^{2} : \frac{- 3 x ^{3} + 18 x}{9 - x ^{2}}

= \frac{- 3 x ^{3} + 18 x}{9 - x ^{2}}

x \to 0 lim (\frac{7 x}{sin ( x )})

d er i v a t i v e f (x) = 5 x + 6

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\frac{d P}{d t} = - \frac{1}{2} P + t

\frac{d y}{d x} = x^{2} sec (y)