derivative f(x)=\sqrt[4]{x^3}

Lösung

ableitung von

f (x) = 4 x^{3}

\frac{3 x ^{2}}{4 ( x ^{3} ) ^{\frac{3}{4}}}

Schritte zur Lösung

\frac{d}{d x} (4 x^{3})

Wende die Kettenregel an:

\frac{1}{4 ( x ^{3} ) ^{\frac{3}{4}}} \frac{d}{d x} (x^{3})

= \frac{1}{4 ( x ^{3} ) ^{\frac{3}{4}}} \frac{d}{d x} (x^{3})

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

= \frac{1}{4 ( x ^{3} ) ^{\frac{3}{4}}} \cdot 3 x^{2}

Vereinfache

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

= \frac{3 x ^{2}}{4 ( x ^{3} ) ^{\frac{3}{4}}}

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

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

n = 1 \sum \infty \frac{n}{n ^{3} + 2}

n = 0 \sum \infty \frac{1}{2 ^{n + 2}}

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