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Beliebt Rechnen >

derivative of 6sqrt(x^7)

Lösung

\frac{d}{d x} (6 x^{7})

Lösung

21 x^{\frac{5}{2}}

Schritte zur Lösung

\frac{d}{d x} (6 x^{7})

Entferne die Konstante:

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

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

Wende Radikal Regel an:

n a^{m} = a^{\frac{m}{n}}

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

Wende die Potenzregel an:

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

= 6 \cdot \frac{7}{2} x^{\frac{7}{2} - 1}

Vereinfache

6 \cdot \frac{7}{2} x^{\frac{7}{2} - 1} : 21 x^{\frac{5}{2}}

= 21 x^{\frac{5}{2}}

Graph

Beliebte Beispiele

derivative of 3ax+bx^3

\frac{d}{d x} (3 a x + b x^{3})

(\partial)/(\partial x)(3x^2+5xy-7y^2+1)

\frac{\partial}{\partial x} (3 x^{2} + 5 x y - 7 y^{2} + 1)

derivative of e^{x^2+4}

\frac{d}{d x} (e^{x^{2} + 4})

integral of x^2(6-x^3)

\int x^{2} (6 - x^{3}) d x

derivative of cos^2(2x+1)

\frac{d}{d x} (cos^{2} (2 x + 1))