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

Lösung

ableitung von

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

54 x^{5} - 60 x^{4} - 200 x^{3} + 216 x^{2} + 114 x - 108

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} ((3 x - 2)^{2}) = 6 (3 x - 2)

\frac{d}{d x} ((3 - x^{2})^{2}) = - 4 x (3 - x^{2})

= 6 (3 x - 2) (3 - x^{2})^{2} + (- 4 x (3 - x^{2})) (3 x - 2)^{2}

Vereinfache

6 (3 x - 2) (3 - x^{2})^{2} + (- 4 x (3 - x^{2})) (3 x - 2)^{2} : 54 x^{5} - 60 x^{4} - 200 x^{3} + 216 x^{2} + 114 x - 108

= 54 x^{5} - 60 x^{4} - 200 x^{3} + 216 x^{2} + 114 x - 108

\int (16 - x^{2}) d x

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

\int \frac{1}{a ^{2} - x ^{2}} d x

t an g e n t y = g (x), at x = 2

d er i v a t i v e g (x) = (4 - 2 x) e^{n} - 4