derivative of xsqrt(3-2x^2)

Lösung

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

\frac{- 4 x ^{2} + 3}{3 - 2 x ^{2}}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

1 \cdot 3 - 2 x^{2} + (- \frac{2 x}{3 - 2 x ^{2}}) x : \frac{- 4 x ^{2} + 3}{3 - 2 x ^{2}}

= \frac{- 4 x ^{2} + 3}{3 - 2 x ^{2}}

\int \frac{u}{u ^{2} - 1} d u

\frac{d N}{d t} = \frac{t e ^{t}}{N ^{2}}

n = 0 \sum \infty \frac{1}{n ^{5}}

n = 8 \sum \infty (\frac{1}{4})^{n}

d er i v a t i v e \frac{7 x ^{2}}{x}