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Beliebt Rechnen >

derivative of (2x^7+5x^3-1/4)

Lösung

\frac{d}{d x} (\frac{2 x ^{7} + 5 x ^{3} - 1}{4})

Lösung

\frac{1}{4} (14 x^{6} + 15 x^{2})

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x ^{7} + 5 x ^{3} - 1}{4})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{4} \frac{d}{d x} (2 x^{7} + 5 x^{3} - 1)

Wende die Summen-/Differenzregel an:

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

= \frac{1}{4} (\frac{d}{d x} (2 x^{7}) + \frac{d}{d x} (5 x^{3}) - \frac{d}{d x} (1))

\frac{d}{d x} (2 x^{7}) = 14 x^{6}

\frac{d}{d x} (5 x^{3}) = 15 x^{2}

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

= \frac{1}{4} (14 x^{6} + 15 x^{2} - 0)

Vereinfache

= \frac{1}{4} (14 x^{6} + 15 x^{2})

Graph

Beliebte Beispiele

integral from 0 to pi of (1+sin(x))

\int_{0}^{π} (1 + sin (x)) d x

2y^{'''}+3y^{''}-23y^'-12y=0

2 y^{^{'''}} + 3 y^{^{''}} - 23 y^{^{'}} - 12 y = 0

integral of xsin(10x)

\int x sin (10 x) d x

integral of 0.4t

\int 0.4 t d t

limit as x approaches 0 of x^2-4x+2

x \to 0 lim (x^{2} - 4 x + 2)