derivative of (x^4/4-9/2 x^2+1)

Lösung

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

x^{3} - 9 x

Schritte zur Lösung

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

Vereinfache

\frac{x ^{4}}{4} - \frac{9}{2} x^{2} + 1 : \frac{x ^{4}}{4} - \frac{9 x ^{2}}{2} + 1

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (\frac{9 x ^{2}}{2}) = 9 x

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

= x^{3} - 9 x + 0

Vereinfache

= x^{3} - 9 x

\int (x + y)^{2} d x

x \to 0 lim (\frac{sin ( 4 x )}{tan ( 3 x )})

\int_{1}^{\infty} 12 e^{- 6 x} d x

in v erse l a pl a ce \frac{10 s ^{2}}{s ^{2} + 9}

x \to 1 lim (x^{2} + 5)