derivative f(x)=(3x+4)(5-x^2)(4+x^2)

Lösung

ableitung von

f (x) = (3 x + 4) (5 - x^{2}) (4 + x^{2})

- 15 x^{4} - 16 x^{3} + 9 x^{2} + 8 x + 60

Schritte zur Lösung

\frac{d}{d x} ((3 x + 4) (5 - x^{2}) (4 + x^{2}))

Wende die Produktregel an:

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

f = 3 x + 4, g = (5 - x^{2}) (4 + x^{2})

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

\frac{d}{d x} (3 x + 4) = 3

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

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

Vereinfache

3 (5 - x^{2}) (4 + x^{2}) + (- 4 x^{3} + 2 x) (3 x + 4) : - 15 x^{4} - 16 x^{3} + 9 x^{2} + 8 x + 60

= - 15 x^{4} - 16 x^{3} + 9 x^{2} + 8 x + 60

x \to \infty lim (e^{x} + 3)

\int_{0}^{\infty} e^{- \frac{x}{4}} d x

x \to 0 lim ((1 + x)^{\frac{2}{x}})

\int 5 tan (6 x) sec^{2} (6 x) d x

l a pl a ce t r an s f or m sin (5 t)