derivative f(x)=|x^2-4|

Lösung

ableitung von

f (x) = x^{2} - 4

\frac{2 x ( x ^{2} - 4 )}{∣ x ^{2} - 4 ∣}

Schritte zur Lösung

\frac{d}{d x} (x^{2} - 4)

Wende die Kettenregel an:

\frac{x ^{2} - 4}{∣ ( x ^{2} - 4 ) ∣} \frac{d}{d x} (x^{2} - 4)

= \frac{x ^{2} - 4}{∣ ( x ^{2} - 4 ) ∣} \frac{d}{d x} (x^{2} - 4)

\frac{d}{d x} (x^{2} - 4) = 2 x

= \frac{x ^{2} - 4}{∣ ( x ^{2} - 4 ) ∣} \cdot 2 x

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 x ( x ^{2} - 4 )}{∣ x ^{2} - 4 ∣}

x \to - 6 + lim (\frac{1}{( x + 6 ) ^{4}})

- 2 y^{2} d y = y^{3} v d v

x \to 4 lim ((5 x + 7)^{4})

\int \frac{4 x ^{3} + 2 x ^{2} + 8}{( x ^{2} + 4 ) ^{2}} d x

\frac{d}{d x} (\frac{( ln ( x ) ) ^{2}}{e ^{x}})