(\partial)/(\partial x)(x^2z+y,x+y,y+z^2)

Lösung

\frac{\partial}{\partial x} (x^{2} z + y, x + y, y + z^{2})

2 z x + (y, 1) + 0 + 0

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} z + y, x + y, y + z^{2})

Behandle

z, y

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{2} z) + \frac{\partial}{\partial x} (y, x) + \frac{\partial}{\partial x} (y, y) + \frac{\partial}{\partial x} (z^{2})

\frac{\partial}{\partial x} (x^{2} z) = 2 z x

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

\frac{\partial}{\partial x} (y, y) = 0

\frac{\partial}{\partial x} (z^{2}) = 0

= 2 z x + (y, 1) + 0 + 0

4 x^{2} \frac{d y}{d x} = \frac{d y}{d x} + 9 x e^{- y}

d er i v a t i v e x^{2} - 2 x + 3

t an g e n t f (x) = \frac{3 x}{x ^{2} - 6}, 3, at x = 3

d er i v a t i v e \frac{8 5}{15} x^{\frac{3}{2}} - 2

\int cos^{3} (7 x) sin^{- 2} (7 x) d x