(\partial)/(\partial x)(f(x,y)x(x,y))

Lösung

\frac{\partial}{\partial x} (f (x, y) x (x, y))

\frac{\partial}{\partial x} (f (x, y)) x (x, y) + (1 \cdot (x, y) + (, y \cdot 1) x) f (x, y)

Schritte zur Lösung

\frac{\partial}{\partial x} (f (x, y) x (x, y))

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = f (x, y), g = x (x, y)

= \frac{\partial}{\partial x} (f (x, y)) x (x, y) + \frac{\partial}{\partial x} (x (x, y)) f (x, y)

\frac{\partial}{\partial x} (x (x, y)) = 1 \cdot (x, y) + (, y \cdot 1) x

= \frac{\partial}{\partial x} (f (x, y)) x (x, y) + (1 \cdot (x, y) + (, y \cdot 1) x) f (x, y)

\frac{d y}{d x} = 8 y

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

\int_{0}^{l n (3)} \frac{3}{e ^{x} + 2} d x

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

t an g e n t y = 9 x - 8 x, (1, 1)