derivative f(x)=\sqrt[5]{x^4}-2/x

Lösung

ableitung von

f (x) = 5 x^{4} - \frac{2}{x}

\frac{4 x ^{3}}{5 ( x ^{4} ) ^{\frac{4}{5}}} + \frac{2}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (5 x^{4} - \frac{2}{x})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (5 x^{4}) - \frac{d}{d x} (\frac{2}{x})

\frac{d}{d x} (5 x^{4}) = \frac{4 x ^{3}}{5 ( x ^{4} ) ^{\frac{4}{5}}}

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

= \frac{4 x ^{3}}{5 ( x ^{4} ) ^{\frac{4}{5}}} - (- \frac{2}{x ^{2}})

Vereinfache

= \frac{4 x ^{3}}{5 ( x ^{4} ) ^{\frac{4}{5}}} + \frac{2}{x ^{2}}

d er i v a t i v e y = \frac{a ^{4}}{a ^{3} - 8 x}

\frac{\partial}{\partial z} (z y^{2} (t + 1))

\int \frac{sec ( y )}{sin ( y )} d y

\frac{\partial}{\partial x} (\frac{1}{x ^{2}})

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