derivative y=(x^6-7x+4)(x^4-5x)

Lösung

ableitung von

y = (x^{6} - 7 x + 4) (x^{4} - 5 x)

10 x^{9} - 35 x^{6} - 35 x^{4} + 16 x^{3} + 70 x - 20

Schritte zur Lösung

\frac{d}{d x} ((x^{6} - 7 x + 4) (x^{4} - 5 x))

Wende die Produktregel an:

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

f = x^{6} - 7 x + 4, g = x^{4} - 5 x

= \frac{d}{d x} (x^{6} - 7 x + 4) (x^{4} - 5 x) + \frac{d}{d x} (x^{4} - 5 x) (x^{6} - 7 x + 4)

\frac{d}{d x} (x^{6} - 7 x + 4) = 6 x^{5} - 7

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

= (6 x^{5} - 7) (x^{4} - 5 x) + (4 x^{3} - 5) (x^{6} - 7 x + 4)

Vereinfache

(6 x^{5} - 7) (x^{4} - 5 x) + (4 x^{3} - 5) (x^{6} - 7 x + 4) : 10 x^{9} - 35 x^{6} - 35 x^{4} + 16 x^{3} + 70 x - 20

= 10 x^{9} - 35 x^{6} - 35 x^{4} + 16 x^{3} + 70 x - 20

(\frac{y}{x} + 3 x) d x + (ln (x) - 2) d y = 0

\int_{0}^{π} x sin (x) d x

\frac{\partial}{\partial x} (\frac{8 y}{x ^{5}})

f (x) = \frac{1}{2 x + 1}

t an g e n t f (x) = \frac{2 x - 4}{x}, at x = 4