derivative of x{f}(x+{f}(x)(cx)+c{f}(x))

Lösung

\frac{d}{d x} (x f (x) + f (x) (c x) + c f (x))

f (x) + x \frac{d}{d x} (f (x)) + c (x \frac{d}{d x} (f (x)) + f (x)) + c \frac{d}{d x} (f (x))

Schritte zur Lösung

\frac{d}{d x} (x f (x) + f (x) (c x) + c f (x))

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x f (x)) + \frac{d}{d x} (f (x) c x) + \frac{d}{d x} (c f (x))

\frac{d}{d x} (x f (x)) = f (x) + x \frac{d}{d x} (f (x))

\frac{d}{d x} (f (x) c x) = c (x \frac{d}{d x} (f (x)) + f (x))

\frac{d}{d x} (c f (x)) = c \frac{d}{d x} (f (x))

= f (x) + x \frac{d}{d x} (f (x)) + c (x \frac{d}{d x} (f (x)) + f (x)) + c \frac{d}{d x} (f (x))

\int_{1}^{2} - x + \frac{85}{50} d x

\int tan^{2} (x) \cdot sec^{3} (x) d x

\frac{\partial}{\partial x} (ln (x + 4 y + 9 z))

t an g e n t y = 6 x - x^{2}, (1, 5)

\int \frac{x + 2}{x ^{2} + 9} d x