derivative f(x)=x^3(x-9)^2

Lösung

ableitung von

f (x) = x^{3} (x - 9)^{2}

5 x^{4} - 72 x^{3} + 243 x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{3}, g = (x - 9)^{2}

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

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

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

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

Vereinfache

3 x^{2} (x - 9)^{2} + 2 (x - 9) x^{3} : 5 x^{4} - 72 x^{3} + 243 x^{2}

= 5 x^{4} - 72 x^{3} + 243 x^{2}

\frac{d}{d x} (6 x^{5} - 15 x^{4} + 30 x^{2} - 30 x + 9)

n = 2 \sum \infty \frac{1}{n ( ln ( n ) )}

\frac{d}{d x} (2 x^{3} + 3 x^{2} - 36 x)

in v erse l a pl a ce \frac{s}{s ^{2}}

\int \frac{ln ( x )}{x 1 + ln ( x )} d x