derivative of x^{4/3}-4x^{1/3}+1

Lösung

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

\frac{4 x - 4}{3 x ^{\frac{2}{3}}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

\frac{d}{d x} (1) = 0

= \frac{4 x ^{\frac{1}{3}}}{3} - \frac{4}{3 x ^{\frac{2}{3}}} + 0

Vereinfache

\frac{4 x ^{\frac{1}{3}}}{3} - \frac{4}{3 x ^{\frac{2}{3}}} + 0 : \frac{4 x - 4}{3 x ^{\frac{2}{3}}}

= \frac{4 x - 4}{3 x ^{\frac{2}{3}}}

\frac{\partial}{\partial x} (cos (4 y - x))

\frac{\partial}{\partial x} (4 y^{x})

t an g e n t 9 x - 9 x

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

\int sin (x) in (cos (x)) d x