derivative f(x)=|x^2-25|

Lösung

ableitung von

f (x) = x^{2} - 25

\frac{2 x ( x ^{2} - 25 )}{∣ x ^{2} - 25 ∣}

Schritte zur Lösung

\frac{d}{d x} (x^{2} - 25)

Wende die Kettenregel an:

\frac{x ^{2} - 25}{∣ ( x ^{2} - 25 ) ∣} \frac{d}{d x} (x^{2} - 25)

= \frac{x ^{2} - 25}{∣ ( x ^{2} - 25 ) ∣} \frac{d}{d x} (x^{2} - 25)

\frac{d}{d x} (x^{2} - 25) = 2 x

= \frac{x ^{2} - 25}{∣ ( x ^{2} - 25 ) ∣} \cdot 2 x

Multipliziere Brüche:

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

= \frac{2 x ( x ^{2} - 25 )}{∣ x ^{2} - 25 ∣}

x \to 0 lim (\frac{sin ( 6 x )}{sin ( 9 x )})

t y^{^{'}} + (t + 1) y = t, y (ln (7)) = 1

\frac{d}{d x} (5 x^{3} + 2 ln (x))

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

x \to 3 lim (4 x^{2} + 1)