derivative of x(x^5+9^3)

Lösung

\frac{d}{d x} (x (x^{5} + 9)^{3})

(x^{5} + 9)^{3} + 15 x^{5} (x^{5} + 9)^{2}

Schritte zur Lösung

\frac{d}{d x} (x (x^{5} + 9)^{3})

Wende die Produktregel an:

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

f = x, g = (x^{5} + 9)^{3}

= \frac{d x}{d x} (x^{5} + 9)^{3} + \frac{d}{d x} ((x^{5} + 9)^{3}) x

\frac{d x}{d x} = 1

\frac{d}{d x} ((x^{5} + 9)^{3}) = 15 x^{4} (x^{5} + 9)^{2}

= 1 \cdot (x^{5} + 9)^{3} + 15 x^{4} (x^{5} + 9)^{2} x

Vereinfache

1 \cdot (x^{5} + 9)^{3} + 15 x^{4} (x^{5} + 9)^{2} x : (x^{5} + 9)^{3} + 15 x^{5} (x^{5} + 9)^{2}

= (x^{5} + 9)^{3} + 15 x^{5} (x^{5} + 9)^{2}

t an g e n t y = x^{4} - 5 x^{3} + 3 x^{2} - 4 x, (- 1, 13)

\frac{d y}{d x} = \frac{x y + x}{y}

x \to 1000 lim (x^{\frac{2}{3}})

\frac{d}{d x} (\frac{1}{3} x^{3} - 5 x - \frac{4}{x})

\int x \cdot ln^{5} (x) d x