derivative of 5xsqrt(x)

Lösung

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

\frac{15 x}{2}

Schritte zur Lösung

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

Vereinfache

5 x x : 5 x^{\frac{3}{2}}

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

Entferne die Konstante:

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

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

Wende die Potenzregel an:

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

= 5 \cdot \frac{3}{2} x^{\frac{3}{2} - 1}

Vereinfache

5 \cdot \frac{3}{2} x^{\frac{3}{2} - 1} : \frac{15 x}{2}

= \frac{15 x}{2}

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

\int_{0}^{\frac{π}{4}} cos (x) d x

\frac{d}{d x} (20 x^{- 8} + 5 x^{- 3} - 7 x^{- 7})

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

\frac{d}{d x} ((1 - x^{2})^{10})