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Beliebt Rechnen >

derivative of (x^5-5x/5)

Lösung

\frac{d}{d x} (\frac{x ^{5} - 5 x}{5})

Lösung

x^{4} - 1

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{5} - 5 x}{5})

Entferne die Konstante:

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

= \frac{1}{5} \frac{d}{d x} (x^{5} - 5 x)

Wende die Summen-/Differenzregel an:

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

= \frac{1}{5} (\frac{d}{d x} (x^{5}) - \frac{d}{d x} (5 x))

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (5 x) = 5

= \frac{1}{5} (5 x^{4} - 5)

Vereinfache

\frac{1}{5} (5 x^{4} - 5) : x^{4} - 1

= x^{4} - 1

Graph

Beliebte Beispiele

integral of x/(a+bx^2)

\int \frac{x}{a + b x ^{2}} d x

derivative of x^3+x^5

\frac{d}{d x} (x^{3} + x^{5})

derivative of in^4x

\frac{d}{d x} (i n^{4} x)

derivative x^2-x+1

d er i v a t i v e x^{2} - x + 1

(\partial)/(\partial x)(sqrt(2)x)

\frac{\partial}{\partial x} (2 x)