derivative x(10-2x)(16-2x)

Lösung

ableitung von

x (10 - 2 x) (16 - 2 x)

12 x^{2} - 104 x + 160

Schritte zur Lösung

\frac{d}{d x} (x (10 - 2 x) (16 - 2 x))

Wende die Produktregel an:

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

f = x, g = (10 - 2 x) (16 - 2 x)

= \frac{d x}{d x} (10 - 2 x) (16 - 2 x) + \frac{d}{d x} ((10 - 2 x) (16 - 2 x)) x

\frac{d x}{d x} = 1

\frac{d}{d x} ((10 - 2 x) (16 - 2 x)) = 8 x - 52

= 1 \cdot (10 - 2 x) (16 - 2 x) + (8 x - 52) x

Vereinfache

1 \cdot (10 - 2 x) (16 - 2 x) + (8 x - 52) x : 12 x^{2} - 104 x + 160

= 12 x^{2} - 104 x + 160

y^{^{'}} + 2 y = e^{x}

\frac{\partial}{\partial x} (z^{3})

\frac{\partial}{\partial s} (s t - 3)

\frac{\partial}{\partial x} (x^{2} + 2 y^{2} - 1)

\int \frac{x ^{2}}{2 - x ^{2}} d x