derivative of 3x^2sqrt(x)

Lösung

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

\frac{15 x ^{\frac{3}{2}}}{2}

Schritte zur Lösung

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

Vereinfache

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

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

Entferne die Konstante:

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

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

Wende die Potenzregel an:

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

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

Vereinfache

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

= \frac{15 x ^{\frac{3}{2}}}{2}

x \to 0 lim (\frac{5}{cos ( 5 x )})

\frac{\partial}{\partial x} (3 x y - x^{2} y)

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

\frac{\partial}{\partial x} (cos (ln (x)))

d er i v a t i v e f (x) = x^{2} - 3 x + 3