(\partial)/(\partial x)(xy(1-7x-4y))

Lösung

\frac{\partial}{\partial x} (x y (1 - 7 x - 4 y))

y (- 14 x - 4 y + 1)

Schritte zur Lösung

\frac{\partial}{\partial x} (x y (1 - 7 x - 4 y))

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= y \frac{\partial}{\partial x} (x (1 - 7 x - 4 y))

Wende die Produktregel an:

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

f = x, g = 1 - 7 x - 4 y

= y (\frac{\partial}{\partial x} (x) (1 - 7 x - 4 y) + \frac{\partial}{\partial x} (1 - 7 x - 4 y) x)

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (1 - 7 x - 4 y) = - 7

= y (1 \cdot (1 - 7 x - 4 y) + (- 7) x)

Vereinfache

y (1 \cdot (1 - 7 x - 4 y) + (- 7) x) : y (- 14 x - 4 y + 1)

= y (- 14 x - 4 y + 1)

a re a 8 cos (2 x), 8 - 8 cos (2 x), 0, \frac{π}{2}

x \to 0 + lim (x - \frac{1}{x ^{3}})

\frac{\partial}{\partial x} (ln (1 + x^{2} + e^{y} + z))

t an g e n t y = sec (x), (\frac{π}{6}, \frac{2 3}{3})

2 x y^{^{'}} - 8 y = x^{- 4}