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

Lösung

ableitung von

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

9 x^{2} - 5 x^{4}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{3}, g = 3 - x^{2}

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

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

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

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

Vereinfache

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

= 9 x^{2} - 5 x^{4}

d er i v a t i v e f (x) = \frac{x}{x ^{2} - 7}

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

n \to 2 lim (\frac{1}{n ^{2}})

x \to 2 + lim (x^{2} - 4)

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