derivative of x^3(x-7^2)

Lösung

\frac{d}{d x} (x^{3} (x - 7)^{2})

5 x^{4} - 56 x^{3} + 147 x^{2}

Schritte zur Lösung

\frac{d}{d x} (x^{3} (x - 7)^{2})

Wende die Produktregel an:

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

f = x^{3}, g = (x - 7)^{2}

= \frac{d}{d x} (x^{3}) (x - 7)^{2} + \frac{d}{d x} ((x - 7)^{2}) x^{3}

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

\frac{d}{d x} ((x - 7)^{2}) = 2 (x - 7)

= 3 x^{2} (x - 7)^{2} + 2 (x - 7) x^{3}

Vereinfache

3 x^{2} (x - 7)^{2} + 2 (x - 7) x^{3} : 5 x^{4} - 56 x^{3} + 147 x^{2}

= 5 x^{4} - 56 x^{3} + 147 x^{2}

a re a y = x^{2} - 4 x + 3, y = 3 + 4 x - x^{2}

x \to - \infty lim (e^{x})

d er i v a t i v e cos (\frac{π x}{4})

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

a re a x = 3 y, x = y^{2} - 4