derivative xsqrt(3-x^2)

Lösung

ableitung von

x 3 - x^{2}

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = 3 - x^{2}

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

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

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

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

Vereinfache

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

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

x \to 2 lim (\frac{1}{∣ 2 - x ∣})

a re a y = - x^{2} + 8 x - 12, y = x^{2} - 8 x + 18, x = 3 x = 6

t an g e n t f (x) = 6 x^{2} + 4 x - 7, - 3

\int \frac{( arcsin ( \frac{x}{3} ) ) ^{2}}{9 - x ^{2}} d x

\frac{\partial}{\partial y} ((x - y)^{5})