derivative of 1/2 x^4-2x^2

Lösung

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

2 x^{3} - 4 x

Schritte zur Lösung

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

Vereinfache

\frac{1}{2} x^{4} - 2 x^{2} : \frac{x ^{4}}{2} - 2 x^{2}

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

Wende die Summen-/Differenzregel an:

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

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

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

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

= 2 x^{3} - 4 x

x \to 3 lim (\frac{x ^{3} - 9}{x - 3})

d er i v a t i v e (8 (2 x)^{4} + 5)^{3}

\frac{\partial}{\partial x} ((x^{p} + y^{p})^{\frac{1}{p}})

t an g e n t \frac{1}{5 + 3 x}

\int \frac{1}{x ln ( x ^{8} )} d x