derivative of xsqrt(6-x^2)

Lösung

\frac{d}{d x} (x 6 - x^{2})

\frac{- 2 x ^{2} + 6}{6 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (x 6 - x^{2})

Wende die Produktregel an:

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

f = x, g = 6 - x^{2}

= \frac{d x}{d x} 6 - x^{2} + \frac{d}{d x} (6 - x^{2}) x

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

\frac{d}{d x} (6 - x^{2}) = - \frac{x}{6 - x ^{2}}

= 1 \cdot 6 - x^{2} + (- \frac{x}{6 - x ^{2}}) x

Vereinfache

1 \cdot 6 - x^{2} + (- \frac{x}{6 - x ^{2}}) x : \frac{- 2 x ^{2} + 6}{6 - x ^{2}}

= \frac{- 2 x ^{2} + 6}{6 - x ^{2}}

\int - 2 sin (t) d t

n = 2 \sum \infty \frac{7}{2 ^{n}}

\int_{0}^{1} \frac{32}{x ^{2} - 64} d x

in v erse l a pl a ce \frac{1}{s ^{2} \cdot ( s + 1 )}

d er i v a t i v e f (x) = \frac{7}{2} x^{\frac{2}{7}}