derivative of (x^3+x^2-2(7+x-x^4))

Lösung

\frac{d}{d x} ((x^{3} + x^{2} - 2) (7 + x - x^{4}))

- 7 x^{6} - 6 x^{5} + 12 x^{3} + 24 x^{2} + 14 x - 2

Schritte zur Lösung

\frac{d}{d x} ((x^{3} + x^{2} - 2) (7 + x - x^{4}))

Wende die Produktregel an:

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

f = x^{3} + x^{2} - 2, g = 7 + x - x^{4}

= \frac{d}{d x} (x^{3} + x^{2} - 2) (7 + x - x^{4}) + \frac{d}{d x} (7 + x - x^{4}) (x^{3} + x^{2} - 2)

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

\frac{d}{d x} (7 + x - x^{4}) = - 4 x^{3} + 1

= (3 x^{2} + 2 x) (7 + x - x^{4}) + (- 4 x^{3} + 1) (x^{3} + x^{2} - 2)

Vereinfache

(3 x^{2} + 2 x) (7 + x - x^{4}) + (- 4 x^{3} + 1) (x^{3} + x^{2} - 2) : - 7 x^{6} - 6 x^{5} + 12 x^{3} + 24 x^{2} + 14 x - 2

= - 7 x^{6} - 6 x^{5} + 12 x^{3} + 24 x^{2} + 14 x - 2

\int \frac{( 3 ( 4 u + 1 ) ^{\frac{1}{2}} )}{4} d u

\frac{d}{d x} (3 arccos (\frac{x}{2}))

\int \frac{42 w ^{7} - 7 w}{7 w ^{5}} d w

s l o p e in t erce pt (4, 0), (- 2, 4)

y^{^{''}} + 4 y^{^{'}} + 3 y = 4 e^{- t}, y (0) = 0, y^{^{'}} (0) = 2