derivative of x^3(x-1^2)

Lösung

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

5 x^{4} - 8 x^{3} + 3 x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{3}, g = (x - 1)^{2}

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

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

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

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

Vereinfache

3 x^{2} (x - 1)^{2} + 2 (x - 1) x^{3} : 5 x^{4} - 8 x^{3} + 3 x^{2}

= 5 x^{4} - 8 x^{3} + 3 x^{2}

t an g e n t y = (3 x + x) (2 - x^{2})

\frac{d}{d x} (13 x^{2} - 5 x + 8)

7 y^{^{'}} + 1 y = 8 e^{3} x, y (0) = 9

f (x) = sin (3 x) cos (5 x)

\frac{d}{d t} (\frac{t + π}{t} cos (t))