derivative of (6x^5-4x^4+7x(x^3-x^2-1))

Lösung

\frac{d}{d x} ((6 x^{5} - 4 x^{4} + 7 x) (x^{3} - x^{2} - 1))

48 x^{7} - 70 x^{6} + 24 x^{5} - 30 x^{4} + 44 x^{3} - 21 x^{2} - 7

Schritte zur Lösung

\frac{d}{d x} ((6 x^{5} - 4 x^{4} + 7 x) (x^{3} - x^{2} - 1))

Wende die Produktregel an:

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

f = 6 x^{5} - 4 x^{4} + 7 x, g = x^{3} - x^{2} - 1

= \frac{d}{d x} (6 x^{5} - 4 x^{4} + 7 x) (x^{3} - x^{2} - 1) + \frac{d}{d x} (x^{3} - x^{2} - 1) (6 x^{5} - 4 x^{4} + 7 x)

\frac{d}{d x} (6 x^{5} - 4 x^{4} + 7 x) = 30 x^{4} - 16 x^{3} + 7

\frac{d}{d x} (x^{3} - x^{2} - 1) = 3 x^{2} - 2 x

= (30 x^{4} - 16 x^{3} + 7) (x^{3} - x^{2} - 1) + (3 x^{2} - 2 x) (6 x^{5} - 4 x^{4} + 7 x)

Vereinfache

(30 x^{4} - 16 x^{3} + 7) (x^{3} - x^{2} - 1) + (3 x^{2} - 2 x) (6 x^{5} - 4 x^{4} + 7 x) : 48 x^{7} - 70 x^{6} + 24 x^{5} - 30 x^{4} + 44 x^{3} - 21 x^{2} - 7

= 48 x^{7} - 70 x^{6} + 24 x^{5} - 30 x^{4} + 44 x^{3} - 21 x^{2} - 7

\frac{\partial}{\partial x} (e^{x + y + 5})

\frac{\partial}{\partial z} (\frac{x - y}{x + z})

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{t}}{1 + t ^{2}}

\int_{0}^{π} sin^{4} (3 x) d x

\int - 1 d x