derivative f(x)=4x^3(2x^2-3x^3)

Lösung

ableitung von

f (x) = 4 x^{3} (2 x^{2} - 3 x^{3})

4 (- 18 x^{5} + 10 x^{4})

Schritte zur Lösung

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

Entferne die Konstante:

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

= 4 \frac{d}{d x} (x^{3} (2 x^{2} - 3 x^{3}))

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} (2 x^{2} - 3 x^{3}) = 4 x - 9 x^{2}

= 4 (3 x^{2} (2 x^{2} - 3 x^{3}) + (4 x - 9 x^{2}) x^{3})

Multipliziere aus

3 x^{2} (2 x^{2} - 3 x^{3}) + (4 x - 9 x^{2}) x^{3} : - 18 x^{5} + 10 x^{4}

= 4 (- 18 x^{5} + 10 x^{4})

\int sec^{2} (x) tan^{8} (x) d x

(3 x + 4)^{^{'}}

\int \frac{1}{x ^{4}} \cdot x^{5} e^{x} d x

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

\frac{d}{d x} (e^{x^{2} + 6})