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

Lösung

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

\frac{3 x ^{2}}{4} + 1

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d x}{d x} = 1

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

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

Vereinfache

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

x \to 3 lim (4 x^{2} - 2 x + 1)

s l o p e (- 5.1) (- 4.2)

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

in v erse l a pl a ce \frac{5}{s ( s + 3 )}

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