derivative f(x)=\sqrt[4]{x^7}

Lösung

ableitung von

f (x) = 4 x^{7}

\frac{7 x ^{6}}{4 ( x ^{7} ) ^{\frac{3}{4}}}

Schritte zur Lösung

\frac{d}{d x} (4 x^{7})

Wende die Kettenregel an:

\frac{1}{4 ( x ^{7} ) ^{\frac{3}{4}}} \frac{d}{d x} (x^{7})

= \frac{1}{4 ( x ^{7} ) ^{\frac{3}{4}}} \frac{d}{d x} (x^{7})

\frac{d}{d x} (x^{7}) = 7 x^{6}

= \frac{1}{4 ( x ^{7} ) ^{\frac{3}{4}}} \cdot 7 x^{6}

Vereinfache

\frac{1}{4 ( x ^{7} ) ^{\frac{3}{4}}} \cdot 7 x^{6} : \frac{7 x ^{6}}{4 ( x ^{7} ) ^{\frac{3}{4}}}

= \frac{7 x ^{6}}{4 ( x ^{7} ) ^{\frac{3}{4}}}

\frac{d y}{d x} = \frac{y ^{2}}{x}

\int 4 x^{3} e^{- 5 x} d x

in v erse l a pl a ce \frac{1}{( s + 1 ) ( s ^{2} + 2 s + 10 )}

\frac{d}{d x} (\frac{9 x ^{2} + 4}{x ^{2} + 1})

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