derivative f(x)=(1-x)(x^2-7)^2

Lösung

ableitung von

f (x) = (1 - x) (x^{2} - 7)^{2}

- 5 x^{4} + 4 x^{3} + 42 x^{2} - 28 x - 49

Schritte zur Lösung

\frac{d}{d x} ((1 - x) (x^{2} - 7)^{2})

Wende die Produktregel an:

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

f = 1 - x, g = (x^{2} - 7)^{2}

= \frac{d}{d x} (1 - x) (x^{2} - 7)^{2} + \frac{d}{d x} ((x^{2} - 7)^{2}) (1 - x)

\frac{d}{d x} (1 - x) = - 1

\frac{d}{d x} ((x^{2} - 7)^{2}) = 4 x (x^{2} - 7)

= (- 1) (x^{2} - 7)^{2} + 4 x (x^{2} - 7) (1 - x)

Vereinfache

(- 1) (x^{2} - 7)^{2} + 4 x (x^{2} - 7) (1 - x) : - 5 x^{4} + 4 x^{3} + 42 x^{2} - 28 x - 49

= - 5 x^{4} + 4 x^{3} + 42 x^{2} - 28 x - 49

in v erse l a pl a ce \frac{10}{s ( s ^{2} + 8 s + 25 )}

\frac{\partial}{\partial x} (x arctan (yz))

x \to 0 lim (\frac{sin ( \frac{x}{2} )}{x})

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

y^{^{''}} - 4 y^{^{'}} + 3 y = 0, y (0) = 2, y^{^{'}} (0) = 3