derivative of 3x^3(sqrt(x)-2)

Lösung

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

3 (3 x^{2} (x - 2) + \frac{x ^{\frac{5}{2}}}{2})

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = x - 2

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

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

\frac{d}{d x} (x - 2) = \frac{1}{2 x}

= 3 (3 x^{2} (x - 2) + \frac{1}{2 x} x^{3})

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

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

\int_{0}^{1} x^{7} x^{4} + 1 d x

\frac{d y}{d x} = \frac{e ^{x} - 1}{e ^{y}}

\int_{1}^{4} \frac{x ^{2} - 1}{x} d x

x \to 9 lim (\frac{5 x}{x - 9})

t an g e n t f (x) = ((x^{2} + 7) (5 - x))