d/(dt)(\sqrt[3]{t^3+s}+\sqrt[3]{s^3+t})

Lösung

\frac{d}{d t} (3 t^{3} + s + 3 s^{3} + t)

\frac{t ^{2}}{( t ^{3} + s ) ^{\frac{2}{3}}} + \frac{1}{3 ( s ^{3} + t ) ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{d}{d t} (3 t^{3} + s + 3 s^{3} + t)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (3 t^{3} + s) + \frac{d}{d t} (3 s^{3} + t)

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

\frac{d}{d t} (3 s^{3} + t) = \frac{1}{3 ( s ^{3} + t ) ^{\frac{2}{3}}}

= \frac{t ^{2}}{( t ^{3} + s ) ^{\frac{2}{3}}} + \frac{1}{3 ( s ^{3} + t ) ^{\frac{2}{3}}}

\int (1 + x + x^{2} + x^{3}) d x

\int \frac{( 5 x ^{2} - 12 )}{( x ^{2} - 6 x + 13 ) ^{2}} d x

n = 1 \sum \infty \frac{1}{1 + n}

\frac{d}{d y} (y^{2} + 1)

x \to 3 lim (\frac{2}{3 - 2})