derivative of ((x^2+2/3)^2)

Lösung

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

\frac{4 x ( x ^{2} + 2 )}{9}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

2 \cdot \frac{x ^{2} + 2}{3} \cdot \frac{2 x}{3} : \frac{4 x ( x ^{2} + 2 )}{9}

= \frac{4 x ( x ^{2} + 2 )}{9}

s l o p e (3, 2), (- 3, - 2)

roo t s A e^{x}

d er i v a t i v e f (x) = sec (x) tan (x)

\frac{d}{d x} (- 4 cos (x) + sin (x))

t an g e n t f (x) = \frac{x}{( 4 x - 3 ) ^{8}}, at x = 1