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

Lösung

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

\frac{2 ( - 12 x ^{4} + 6 x ^{2} )}{2 - 3 x ^{2}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

2 (3 x^{2} 2 - 3 x^{2} + (- \frac{3 x}{2 - 3 x ^{2}}) x^{3}) : \frac{2 ( - 12 x ^{4} + 6 x ^{2} )}{2 - 3 x ^{2}}

= \frac{2 ( - 12 x ^{4} + 6 x ^{2} )}{2 - 3 x ^{2}}

\frac{d}{d x} (h (g (x) k (x)))

\int (x^{3} + 4 x)^{2} (3 x^{2} + 4) d x

\int \frac{x ^{3} + 7}{x ^{2} + 5 x + 6} d x

\frac{\partial}{\partial x} (4 x^{2} + 4 y + 2 z^{2})

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