derivative of x^2(3x-4^3)

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

\int_{0}^{1} x^{2} e^{x} d x

a re a y = \frac{16}{x ^{2} - 6 x - 55}, y = 0, x = - 3, x = 3

d er i v a t i v e t^{5} - \frac{1}{4 t ^{7}}

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

\frac{d}{d x} (x^{2} + y^{2} - z)